# Thread: Need a clarification of a differential equation solution

1. ## Need a clarification of a differential equation solution

Hello, so as the title says, i have a differential equation, and i already have a solution with steps. However, I dont really know whats going on in the steps or why do they do what they do in the steps. I know this sounds messy so Im just going to show you.

From step 3 im lost. Please can someone clarify whats going on with the substitution and why do they use it ?

Thanks alot.

2. ## Re: Need a clarification of a differential equation solution

The equation is first order linear, so they multiply both sides by an integrating factor so that the LHS can be written as the derivative of a product. Then the solution can be found by integrating.