## Summary of Separable Equations

### Essential Concepts

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

## Key Equations

• Separable differential equation

${y}^{\prime }=f\left(x\right)g\left(y\right)$
• Solution concentration

$\frac{du}{dt}=\text{INFLOW RATE}-\text{OUTFLOW RATE}$
• Newton’s law of cooling

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