Differential Equations For Dummies
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If you need to find particular solutions to nonhomogeneous differential equations, then you can start with the method of undetermined coefficients. Suppose you face the following nonhomogeneous differential equation:


The method of undetermined coefficients notes that when you find a candidate solution, y, and plug it into the left-hand side of the equation, you end up with g(x). Because g(x) is only a function of x, you can often guess the form of yp(x), up to arbitrary coefficients, and then solve for those coefficients by plugging yp(x) into the differential equation.

This method works because you're dealing only with g(x), and the form of g(x) can often tell you what a particular solution looks like.

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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.

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