Summary of Separable Equations

Essential Concepts

  • A separable differential equation is any equation that can be written in the form [latex]y^{\prime} =f\left(x\right)g\left(y\right)[/latex].
  • The method of separation of variables is used to find the general solution to a separable differential equation.

Key Equations

  • Separable differential equation

    [latex]{y}^{\prime }=f\left(x\right)g\left(y\right)[/latex]
  • Solution concentration

    [latex]\frac{du}{dt}=\text{INFLOW RATE}-\text{OUTFLOW RATE}[/latex]
  • Newton’s law of cooling

    [latex]\frac{dT}{dt}=k\left(T-{T}_{s}\right)[/latex]
Glossary
autonomous differential equation
an equation in which the right-hand side is a function of [latex]y[/latex] alone
separable differential equation
any equation that can be written in the form [latex]y^{\prime} =f\left(x\right)g\left(y\right)[/latex]
separation of variables
a method used to solve a separable differential equation