First, isolate all terms that contain [latex]y[/latex].

We will first add [latex]7x[/latex] to both sides of the equation: [latex]x^{2}y+y=3+7x[/latex]

Then, factor [latex]y[/latex] from both terms on the left side: [latex]y(x^{2}+1)=3+7x[/latex]

Now, divide both sides by [latex]x^{2}+1[/latex]: [latex]y=\frac{3+7x}{x^{2}+1}[/latex]

First, isolate all terms that contain [latex]y[/latex].

We will first subtract [latex]3x^{2}[/latex] from both sides of the equation: [latex]y\cos{x}+x^{3}y=4-3x^{2}[/latex]

Then, factor [latex]y[/latex] from both terms on the left side: [latex]y(\cos{x}+x^{3})=4-3x^{2}[/latex]

Now, divide both sides by [latex]\cos{x}+x^{3}[/latex]:

[latex]y=\dfrac{4-3x^{2}}{(\cos{x}+x^{3})}[/latex]