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The Method of Undetermined Coefficients

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❶A problem arises if a member of a family of the nonhomogeneous term happens to be a solution of the corresponding homogeneous equation.

The Method of Undetermined Coefficients

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Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.

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Wolfram|Alpha can help out in many different cases when it comes to differential equations. Get step-by-step directions on solving exact equations or get help on solving higher-order equations. Even differential equations that are solved with initial conditions are easy to compute.

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Pros and Cons of the Method of Undetermined Coefficients:The method is very easy to perform. However, the limitation of the method of undetermined coefficients is that the non-homogeneous term can only contain simple functions such as,,, and so the trial function can be effectively guessed. I am having trouble figuring out how to find a particular solution to a differential equation using the method of undetermined coefficients. Everything I've found from other sites hasn't worked.

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The central idea of the method of undetermined coefficients is this: Form the most general linear combination of the functions in the family of the nonhomogeneous term d(x), substitute this expression into the given nonhomogeneous differential equation, and solve for . The class of \(g(t)\)’s for which the method works, does include some of the more common functions, however, there are many functions out there for which undetermined coefficients simply won’t work. Second, it is generally only useful for constant coefficient differential equations. The method is .