Nonhomogenous Differential Equation

If a second order differential equation $P(x)y^{\prime \prime }+Q(x)y^{\prime }+R(x)y=G(x)$fails to fulfill $G(x)=0$, it is considered nonhomogenous. The general solution to this equation is of the form

$$y=y\_c+y\_p$$

• $y\_c$ is the general solution to the associated homogenous complementary equation (the same differential equation but with $G(x)\text{set to}0$)
• $y\_p$ is any particular solution to the nonhomogenous differential equation. It can be determined either by the method of undetermined coefficients or the method of variation of parameters.x