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.