Summary of Separable Equations | Calculus II

Module 4: Differential Equations

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