Quiz14Solutions - Math 3323 Fall 2009 Quiz #14 Solutions...

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Math 3323 – Fall 2009 Quiz #14 Solutions Undetermined Coefficient System Version 176 – Fully worked out. Find the general solution of !! y + 7 ! y + 10 y = 176 e 6 t . First, the solution of the corresponding homogeneous d.e !! y + 7 ! y + 10 y = 176 e 6 t is y h = C 1 e ! 2 t + C 2 e ! 5 t . Our initial “guess” at a solution for the nonhomogeneous d.e is y p = Ae 6 t . We check for overlap between this initial guess for y p and our previously obtained y h . In this case, there is none, so no modification of our y p is needed. Final “guess”: y p = Ae 6 t . Plugging y p into the nonhomogeneous d.e. and matching coefficients yields 88 A = 176 , so A = 2 . Thus y p = 2 e 6 t , and the general solution to the nonhomogeneous d.e is y = C 1 e ! 2 t + C 2 e ! 5 t + 2 e 6 t . The other versions work out analogously. In each case, there is no overlap
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Quiz14Solutions - Math 3323 Fall 2009 Quiz #14 Solutions...

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