Unformatted text preview: By the superposition principle, y p ( t ) = ( A cos t + B sin t ) e t + C 2 t 2 + C 1 t + C . 35. Since the roots of the auxiliary equation are r = 4 ± √ 16 − 20 2 = 2 ± i, which are di±erent from 5 and 3 i , a particular solution has the form y p ( t ) = ( A 1 t + A ) cos 3 t + ( B 1 t + B ) sin 3 t + Ce 5 t . (The last term corresponds to e 5 t in the righthand side of the original equation, and the ²rst two come from t sin 3 t − cos 3 t .) 204...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Summation, The Roots, auxiliary equation

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