In order to identify a nonhomogeneous differential equation, you first need to know what a homogeneous differential equation looks like. You also often need to solve one before you can solve the other.
Homogeneous differential equations involve only derivatives of y and terms involving y, and they're set to 0, as in this equation:
Nonhomogeneous differential equations are the same as homogeneous differential equations, except they can have terms involving only x (and constants) on the right side, as in this equation:
You also can write nonhomogeneous differential equations in this format: y'' + p(x)y' + q(x)y = g(x). The general solution of this nonhomogeneous differential equation is
In this solution, c1y1(x) + c2y2(x) is the general solution of the corresponding homogeneous differential equation:
And yp(x) is a specific solution to the nonhomogeneous equation.
Steven Holzner is an award-winning author of science, math, and technical books. He got his training in differential equations at MIT and at Cornell University, where he got his PhD. He has been on the faculty at both MIT and Cornell University, and has written such bestsellers as Physics For Dummies and Physics Workbook For Dummies.
