Consider the nonhomogeneous linear equation
We have seen that the general solution is given by
where is a particular solution and is the general solution of the associated homogeneous equation. We will not discuss the case of non-constant coefficients. Therefore, we will restrict ourself only to the following type of equation:
Using the previous section, we will discuss how to find the general solution of the associated homogeneous equation
Therefore, the only remaining obstacle is to find a particular solution to (NH). In the second order differential equations case, we learned the two methods: Undetermined Coefficients Method and the Variation of Parameters. These two methods are still valid in the general case, but the second one is very hard to carry.
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Author: Mohamed Amine Khamsi