Nonhomogeneous Linear Equations

Consider the nonhomogeneous linear equation

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We have seen that the general solution is given by

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where tex2html_wrap_inline28 is a particular solution and tex2html_wrap_inline30 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:

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Using the previous section, we will discuss how to find the general solution of the associated homogeneous equation

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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.

[Differential Equations] [First Order D.E.] [Second Order D.E.]
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Author: Mohamed Amine Khamsi

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