A Differential Equation is an equation with a function and one or more of its derivatives:

Example:

an equation with the function y and its derivative

## Homogeneous Differential Equations

A first order Differential Equation is Homogeneous when it can be in this form:

We can solve it using Separation of Variables but first we create a new variable

With we can solve the Differential Equation.

Example

**First, get it in form**

Now, we have a function of (y/x).

**Then, substitute **

We’ll get

**Now use Separation of Variables:**

**Put C in ln form with C = ln k**

**Now substitute back **

**We got the solution.**