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:
![image0.png](https://www.dummies.com/wp-content/uploads/257411.image0.png)
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:
![image1.png](https://www.dummies.com/wp-content/uploads/257412.image1.png)
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
![image2.png](https://www.dummies.com/wp-content/uploads/257413.image2.png)
In this solution, c1y1(x) + c2y2(x) is the general solution of the corresponding homogeneous differential equation:
![image3.png](https://www.dummies.com/wp-content/uploads/257414.image3.png)
And yp(x) is a specific solution to the nonhomogeneous equation.