UndeterminedCoefficients

# UndeterminedCoefficients - UNDETERMINED COEFFICIENTS Method...

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UNDETERMINED COEFFICIENTS Method for solving a nonhomogeneous second order differential equation This method is supposed to be simpler than the Variation of Parameters method but is limited to equations where f ( x ) is a polynomial, exponential, sine or cosine. For an alternate method see the document VariationOfParameters.pdf. THE PROBLEM 33. p184 y y x " sin + = 9 2 y y ( ) , '( ) 0 1 0 0 = = THE APPROACH To solve this problem we will find a particular solution y p that satisfies the equation and a complementary solution y c of the associated homogeneous equation y y " + = 9 0 . Then we add the results to obtain the general solution y x y y c p ( ) = + . Finally we apply the initial conditions to determine the final solution. THE PARTICULAR SOLUTION We must search for a value y that can satisfy the equation. We take a hint from the term to the right of the equals sign, sin2 x . We select a trial term which can still have this form when its derivatives are taken: y A x B x p = + sin cos 2

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UndeterminedCoefficients - UNDETERMINED COEFFICIENTS Method...

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