If you need to find particular solutions to nonhomogeneous differential equations, then you can start with the method of undetermined coefficients. Suppose you face the following nonhomogeneous differential equation:

The **method of undetermined coefficients** notes that when you find a candidate solution, *y*, and plug it into the left-hand side of the equation, you end up with *g*(*x*). Because *g*(*x*) is only a function of *x*, you can often guess the form of *y** _{p}*(

*x*), up to arbitrary coefficients, and then solve for those coefficients by plugging

*y*

*(*

_{p}*x*) into the differential equation.

This method works because you're dealing only with *g*(*x*), and the form of *g*(*x*) can often tell you what a particular solution looks like.