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.

Example

Suppose we find the solution y2=Ce2x−2⋅x+3, and we are given the initial condition y=2 when x=1:

So y2=xe2x−2+3.