### 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]**Newtonâ€™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