Advanced Math Solutions – Ordinary Differential Equations Calculator, Separable ODE

Last post, we talked about linear first order differential equations. In this post, we will talk about separable differential equations. A separable differential equation is a nonlinear first order differential equation that can be written in the form:

N(y)\frac{dy}{dx}=M(x)

A separable differential equation is separable if the variables can be separated. Separable differential equations are pretty simple and do not require many steps to solve.

How to solve separable differential equations:

1. Rewrite the differential equation as N(y)dy=M(x)dx
2. Integrate both sides
• Don’t forget to add the unknown constant
3. Solve for y(x)

We will solve the first example step by step (click here):

\frac{dy}{dx}=\frac{3x+1}{4y}

1. Rewrite the differential equation

2. Integrate both sides

3. Solve for y(x)

Here’s another example (click here):

Last example (click here):

I think separable differential equations are the easiest ordinary differential equations. There are very few steps to solve them and they are easy to remember. Memorize the steps and you’ll be good to go!

Until next time,

Leah