{"id":345,"date":"2021-03-25T16:08:01","date_gmt":"2021-03-25T16:08:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus2\/?post_type=chapter&p=345"},"modified":"2021-11-17T02:54:37","modified_gmt":"2021-11-17T02:54:37","slug":"module-4-review-problems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/module-4-review-problems\/","title":{"raw":"Module 4 Review Problems","rendered":"Module 4 Review Problems"},"content":{"raw":"
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True or False?<\/em> Justify your answer with a proof or a counterexample.<\/p>\r\n\r\n

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1.\u00a0<\/strong>The differential equation [latex]y^{\\prime} =3{x}^{2}y-\\cos\\left(x\\right)y^{\\prime}\\prime[\/latex] is linear.<\/div>\r\n<\/div>\r\n<\/div>\r\n
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2.\u00a0<\/strong>The differential equation [latex]y^{\\prime} =x-y[\/latex] is separable.<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"240989\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"240989\"]F[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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3. <\/strong>You can explicitly solve all first-order differential equations by separation or by the method of integrating factors.<\/div>\r\n<\/div>\r\n<\/div>\r\n
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4.\u00a0<\/strong>You can determine the behavior of all first-order differential equations using directional fields or Euler\u2019s method.<\/p>\r\n[reveal-answer q=\"873419\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"873419\"]T[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following problems, find the general solution to the differential equations.<\/p>\r\n\r\n

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5.\u00a0<\/strong>[latex]{y}^{\\prime }={x}^{2}+3{e}^{x}-2x[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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6.\u00a0<\/strong>[latex]y^{\\prime} ={2}^{x}+{\\cos}^{-1}x[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"172772\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"172772\"][latex]y\\left(x\\right)=\\frac{{2}^{x}}{\\text{ln}\\left(2\\right)}+x{\\cos}^{-1}x-\\sqrt{1-{x}^{2}}+C[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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7.\u00a0<\/strong>[latex]y^{\\prime} =y\\left({x}^{2}+1\\right)[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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8.\u00a0<\/strong>[latex]y^{\\prime} ={e}^{\\text{-}y}\\sin{x}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"586393\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"586393\"][latex]y\\left(x\\right)=\\text{ln}\\left(C-\\cos{x}\\right)[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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9.\u00a0<\/strong>[latex]y^{\\prime} =3x - 2y[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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10. <\/strong>[latex]y^{\\prime} =y\\text{ln}y[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"426669\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"426669\"][latex]y\\left(x\\right)={e}^{{e}^{C+x}}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following problems, find the solution to the initial value problem.<\/p>\r\n\r\n

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11.\u00a0<\/strong>[latex]y^{\\prime} =8x-\\text{ln}x - 3{x}^{4},y\\left(1\\right)=5[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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12.\u00a0<\/strong>[latex]y^{\\prime} =3x-\\cos{x}+2,y\\left(0\\right)=4[\/latex]<\/p>\r\n[reveal-answer q=\"642537\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"642537\"][latex]y\\left(x\\right)=4+\\frac{3}{2}{x}^{2}+2x-\\sin{x}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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13.\u00a0<\/strong>[latex]xy^{\\prime} =y\\left(x - 2\\right),y\\left(1\\right)=3[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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14.\u00a0<\/strong>[latex]y^{\\prime} =3{y}^{2}\\left(x+\\cos{x}\\right),y\\left(0\\right)=-2[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"448839\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"448839\"][latex]y\\left(x\\right)=-\\frac{2}{1+3\\left({x}^{2}+2\\sin{x}\\right)}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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15. <\/strong>[latex]\\left(x - 1\\right)y^{\\prime} =y - 2,y\\left(0\\right)=0[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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16.\u00a0<\/strong>[latex]y^{\\prime} =3y-x+6{x}^{2},y\\left(0\\right)=-1[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"989712\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"989712\"][latex]y\\left(x\\right)=-2{x}^{2}-2x-\\frac{1}{3}-\\frac{2}{3}{e}^{3x}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following problems, draw the directional field associated with the differential equation, then solve the differential equation. Draw a sample solution on the directional field.<\/p>\r\n\r\n

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17.\u00a0<\/strong>[latex]y^{\\prime} =2y-{y}^{2}[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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18.\u00a0<\/strong>[latex]y^{\\prime} =\\frac{1}{x}+\\text{ln}x-y[\/latex], for [latex]x>0[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"746100\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"746100\"]\"A<\/span><\/p>\r\n[latex]y\\left(x\\right)=C{e}^{\\text{-}x}+\\text{ln}x[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following problems, use Euler\u2019s Method with [latex]n=5[\/latex] steps over the interval [latex]t=\\left[0,1\\right][\/latex]. Then solve the initial-value problem exactly. How close is your Euler\u2019s Method estimate?<\/p>\r\n\r\n

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19.\u00a0<\/strong>[latex]y^{\\prime} =-4yx,y\\left(0\\right)=1[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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20.\u00a0<\/strong>[latex]y^{\\prime} ={3}^{x}-2y,y\\left(0\\right)=0[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"64398\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"64398\"]Euler: [latex]0.6939[\/latex], exact solution: [latex]y\\left(x\\right)=\\frac{{3}^{x}-{e}^{-2x}}{2+\\text{ln}\\left(3\\right)}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following problems, set up and solve the differential equations.<\/p>\r\n\r\n

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21.\u00a0<\/strong>A car drives along a freeway, accelerating according to [latex]a=5\\sin\\left(\\pi t\\right)[\/latex], where [latex]t[\/latex] represents time in minutes. Find the velocity at any time [latex]t[\/latex], assuming the car starts with an initial speed of [latex]60[\/latex] mph.<\/div>\r\n<\/div>\r\n<\/div>\r\n
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22.\u00a0<\/strong>You throw a ball of mass [latex]2[\/latex] kilograms into the air with an upward velocity of [latex]8[\/latex] m\/s. Find exactly the time the ball will remain in the air, assuming that gravity is given by [latex]g=9.8{\\text{m\/s}}^{2}[\/latex].<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"7129\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"7129\"][latex]\\frac{40}{49}[\/latex] second[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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23.\u00a0<\/strong>You drop a ball with a mass of [latex]5[\/latex] kilograms out an airplane window at a height of [latex]5000[\/latex] m. How long does it take for the ball to reach the ground?<\/div>\r\n<\/div>\r\n<\/div>\r\n
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24.\u00a0<\/strong>You drop the same ball of mass [latex]5[\/latex] kilograms out of the same airplane window at the same height, except this time you assume a drag force proportional to the ball\u2019s velocity, using a proportionality constant of [latex]3[\/latex] and the ball reaches terminal velocity. Solve for the distance fallen as a function of time. How long does it take the ball to reach the ground?<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"717785\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"717785\"][latex]x\\left(t\\right)=5000+\\frac{245}{9}-\\frac{49}{3}t-\\frac{245}{9}{e}^{\\frac{\\text{-}5}{3t}},t=307.8[\/latex] seconds[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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25.\u00a0<\/strong>A drug is administered to a patient every [latex]24[\/latex] hours and is cleared at a rate proportional to the amount of drug left in the body, with proportionality constant [latex]0.2[\/latex]. If the patient needs a baseline level of [latex]5[\/latex] mg to be in the bloodstream at all times, how large should the dose be?<\/div>\r\n<\/div>\r\n<\/div>\r\n
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26.\u00a0<\/strong>A [latex]1000[\/latex] -liter tank contains pure water and a solution of [latex]0.2[\/latex] kg salt\/L is pumped into the tank at a rate of [latex]1[\/latex] L\/min and is drained at the same rate. Solve for total amount of salt in the tank at time [latex]t[\/latex].<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"289880\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"289880\"][latex]T\\left(t\\right)=200\\left(1-{e}^{\\frac{\\text{-}}{1000}}\\right)[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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27.\u00a0<\/strong>You boil water to make tea. When you pour the water into your teapot, the temperature is [latex]100^\\circ C.[\/latex] After [latex]5[\/latex] minutes in your [latex]15^\\circ C[\/latex] room, the temperature of the tea is [latex]85^\\circ C.[\/latex] Solve the equation to determine the temperatures of the tea at time [latex]t[\/latex]. How long must you wait until the tea is at a drinkable temperature [latex]\\left(72^\\circ C\\right)?[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n
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28.\u00a0<\/strong>The human population (in thousands) of Nevada in [latex]1950[\/latex] was roughly [latex]160[\/latex]. If the carrying capacity is estimated at [latex]10[\/latex] million individuals, and assuming a growth rate of [latex]2\\text{%}[\/latex] per year, develop a logistic growth model and solve for the population in Nevada at any time (use [latex]1950[\/latex] as time = 0). What population does your model predict for [latex]2000?[\/latex] How close is your prediction to the true value of [latex]1,998,257?[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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[reveal-answer q=\"740922\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"740922\"][latex]P\\left(t\\right)=\\frac{1600000{e}^{0.02t}}{9840+160{e}^{0.02t}}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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29.\u00a0<\/strong>Repeat the previous problem but use Gompertz growth model. Which is more accurate?<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>","rendered":"
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True or False?<\/em> Justify your answer with a proof or a counterexample.<\/p>\n

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1.\u00a0<\/strong>The differential equation [latex]y^{\\prime} =3{x}^{2}y-\\cos\\left(x\\right)y^{\\prime}\\prime[\/latex] is linear.<\/div>\n<\/div>\n<\/div>\n
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2.\u00a0<\/strong>The differential equation [latex]y^{\\prime} =x-y[\/latex] is separable.<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
F<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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3. <\/strong>You can explicitly solve all first-order differential equations by separation or by the method of integrating factors.<\/div>\n<\/div>\n<\/div>\n
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4.\u00a0<\/strong>You can determine the behavior of all first-order differential equations using directional fields or Euler\u2019s method.<\/p>\n

Show Solution<\/span><\/p>\n
T<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following problems, find the general solution to the differential equations.<\/p>\n

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5.\u00a0<\/strong>[latex]{y}^{\\prime }={x}^{2}+3{e}^{x}-2x[\/latex]<\/div>\n<\/div>\n<\/div>\n
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6.\u00a0<\/strong>[latex]y^{\\prime} ={2}^{x}+{\\cos}^{-1}x[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)=\\frac{{2}^{x}}{\\text{ln}\\left(2\\right)}+x{\\cos}^{-1}x-\\sqrt{1-{x}^{2}}+C[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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7.\u00a0<\/strong>[latex]y^{\\prime} =y\\left({x}^{2}+1\\right)[\/latex]<\/div>\n<\/div>\n<\/div>\n
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8.\u00a0<\/strong>[latex]y^{\\prime} ={e}^{\\text{-}y}\\sin{x}[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)=\\text{ln}\\left(C-\\cos{x}\\right)[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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9.\u00a0<\/strong>[latex]y^{\\prime} =3x - 2y[\/latex]<\/div>\n<\/div>\n<\/div>\n
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10. <\/strong>[latex]y^{\\prime} =y\\text{ln}y[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)={e}^{{e}^{C+x}}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following problems, find the solution to the initial value problem.<\/p>\n

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11.\u00a0<\/strong>[latex]y^{\\prime} =8x-\\text{ln}x - 3{x}^{4},y\\left(1\\right)=5[\/latex]<\/div>\n<\/div>\n<\/div>\n
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12.\u00a0<\/strong>[latex]y^{\\prime} =3x-\\cos{x}+2,y\\left(0\\right)=4[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)=4+\\frac{3}{2}{x}^{2}+2x-\\sin{x}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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13.\u00a0<\/strong>[latex]xy^{\\prime} =y\\left(x - 2\\right),y\\left(1\\right)=3[\/latex]<\/div>\n<\/div>\n<\/div>\n
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14.\u00a0<\/strong>[latex]y^{\\prime} =3{y}^{2}\\left(x+\\cos{x}\\right),y\\left(0\\right)=-2[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)=-\\frac{2}{1+3\\left({x}^{2}+2\\sin{x}\\right)}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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15. <\/strong>[latex]\\left(x - 1\\right)y^{\\prime} =y - 2,y\\left(0\\right)=0[\/latex]<\/div>\n<\/div>\n<\/div>\n
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16.\u00a0<\/strong>[latex]y^{\\prime} =3y-x+6{x}^{2},y\\left(0\\right)=-1[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]y\\left(x\\right)=-2{x}^{2}-2x-\\frac{1}{3}-\\frac{2}{3}{e}^{3x}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following problems, draw the directional field associated with the differential equation, then solve the differential equation. Draw a sample solution on the directional field.<\/p>\n

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17.\u00a0<\/strong>[latex]y^{\\prime} =2y-{y}^{2}[\/latex]<\/div>\n<\/div>\n<\/div>\n
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18.\u00a0<\/strong>[latex]y^{\\prime} =\\frac{1}{x}+\\text{ln}x-y[\/latex], for [latex]x>0[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
\"A<\/span><\/p>\n

[latex]y\\left(x\\right)=C{e}^{\\text{-}x}+\\text{ln}x[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following problems, use Euler\u2019s Method with [latex]n=5[\/latex] steps over the interval [latex]t=\\left[0,1\\right][\/latex]. Then solve the initial-value problem exactly. How close is your Euler\u2019s Method estimate?<\/p>\n

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19.\u00a0<\/strong>[latex]y^{\\prime} =-4yx,y\\left(0\\right)=1[\/latex]<\/div>\n<\/div>\n<\/div>\n
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20.\u00a0<\/strong>[latex]y^{\\prime} ={3}^{x}-2y,y\\left(0\\right)=0[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
Euler: [latex]0.6939[\/latex], exact solution: [latex]y\\left(x\\right)=\\frac{{3}^{x}-{e}^{-2x}}{2+\\text{ln}\\left(3\\right)}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

For the following problems, set up and solve the differential equations.<\/p>\n

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21.\u00a0<\/strong>A car drives along a freeway, accelerating according to [latex]a=5\\sin\\left(\\pi t\\right)[\/latex], where [latex]t[\/latex] represents time in minutes. Find the velocity at any time [latex]t[\/latex], assuming the car starts with an initial speed of [latex]60[\/latex] mph.<\/div>\n<\/div>\n<\/div>\n
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22.\u00a0<\/strong>You throw a ball of mass [latex]2[\/latex] kilograms into the air with an upward velocity of [latex]8[\/latex] m\/s. Find exactly the time the ball will remain in the air, assuming that gravity is given by [latex]g=9.8{\\text{m\/s}}^{2}[\/latex].<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]\\frac{40}{49}[\/latex] second<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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23.\u00a0<\/strong>You drop a ball with a mass of [latex]5[\/latex] kilograms out an airplane window at a height of [latex]5000[\/latex] m. How long does it take for the ball to reach the ground?<\/div>\n<\/div>\n<\/div>\n
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24.\u00a0<\/strong>You drop the same ball of mass [latex]5[\/latex] kilograms out of the same airplane window at the same height, except this time you assume a drag force proportional to the ball\u2019s velocity, using a proportionality constant of [latex]3[\/latex] and the ball reaches terminal velocity. Solve for the distance fallen as a function of time. How long does it take the ball to reach the ground?<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]x\\left(t\\right)=5000+\\frac{245}{9}-\\frac{49}{3}t-\\frac{245}{9}{e}^{\\frac{\\text{-}5}{3t}},t=307.8[\/latex] seconds<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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25.\u00a0<\/strong>A drug is administered to a patient every [latex]24[\/latex] hours and is cleared at a rate proportional to the amount of drug left in the body, with proportionality constant [latex]0.2[\/latex]. If the patient needs a baseline level of [latex]5[\/latex] mg to be in the bloodstream at all times, how large should the dose be?<\/div>\n<\/div>\n<\/div>\n
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26.\u00a0<\/strong>A [latex]1000[\/latex] -liter tank contains pure water and a solution of [latex]0.2[\/latex] kg salt\/L is pumped into the tank at a rate of [latex]1[\/latex] L\/min and is drained at the same rate. Solve for total amount of salt in the tank at time [latex]t[\/latex].<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]T\\left(t\\right)=200\\left(1-{e}^{\\frac{\\text{-}}{1000}}\\right)[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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27.\u00a0<\/strong>You boil water to make tea. When you pour the water into your teapot, the temperature is [latex]100^\\circ C.[\/latex] After [latex]5[\/latex] minutes in your [latex]15^\\circ C[\/latex] room, the temperature of the tea is [latex]85^\\circ C.[\/latex] Solve the equation to determine the temperatures of the tea at time [latex]t[\/latex]. How long must you wait until the tea is at a drinkable temperature [latex]\\left(72^\\circ C\\right)?[\/latex]<\/div>\n<\/div>\n<\/div>\n
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28.\u00a0<\/strong>The human population (in thousands) of Nevada in [latex]1950[\/latex] was roughly [latex]160[\/latex]. If the carrying capacity is estimated at [latex]10[\/latex] million individuals, and assuming a growth rate of [latex]2\\text{%}[\/latex] per year, develop a logistic growth model and solve for the population in Nevada at any time (use [latex]1950[\/latex] as time = 0). What population does your model predict for [latex]2000?[\/latex] How close is your prediction to the true value of [latex]1,998,257?[\/latex]<\/p>\n<\/div>\n

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Show Solution<\/span><\/p>\n
[latex]P\\left(t\\right)=\\frac{1600000{e}^{0.02t}}{9840+160{e}^{0.02t}}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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29.\u00a0<\/strong>Repeat the previous problem but use Gompertz growth model. Which is more accurate?<\/div>\n<\/div>\n<\/div>\n<\/section>\n\n\t\t\t
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