When you have a differential equation in the form

you can bring all the ​y​'s to one side and all the ​x​'s to the other:

The solutions to differential equations will usually contain a constant of integration ​+C. These are called general solutions.

Often, we are given an initial condition, ie the value of ​y​ for a specific ​x, which we can use to solve for ​C. The result is the particular solution.

The easiest differential equations to solve are the ones in the form

as we can simply integrate:

For a differential equation in the form

Multiply both sides by integrating factor (often called ​μ​):

and notice the product rule on the LHS.

Let ​y=vx, then ​v=xy​.

Note: On IB exams you will be told to use the substitution ​y=vx.