9 - Substitutions for Differential Equations - Homogenous

THIS LECTURE IS OPTIONAL. YOU WILL MOST PROBABLY NOT NEED THIS FOR THE TEST, WE WILL ONLY BE DEALING WITH CONSTANT COEFFICIENT ODEs. You can skip this lecture if you feel like it.

When do we have homogenous differential equations?

This is usually the case when we have a differential equation where we can write as a function of .

We substitute for some variable v:

Then, we want to get y out.

Now, we substitute.

Such substitution should leave you with only x and v. If you have any y in the equation, you've made a mistake.

After having only x and v, you solve using any known methods like integration or separation before integration, then substitute in the final result to get back y.

Don't get it? Let's do an example.

10 - Example Substitution - Homogenous Differential Equations

Interactive Graph