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Unformatted text preview: p = Ae-2 t , but this term is already included as part of the homogeneous solution. Hence we try a solution of the form y p = Ate-2 t . We thus want to nd A such that y 00 p-3 y p-10 y p = e-2 t . We compute y p = Ae-2 t-2 Ate-2 t and y 00 p =-4 Ae-2 t + 4 Ate-2 t . Crunching everything through, we get (-4 Ae-2 t + 4 At 3-2 t ) + (-3 Ae-2 t + 6 Ate-2 t ) + (-10 Ate-2 t ) = e-2 t-7 Ae-2 t = e-2 t A =-1 7 Hence y = y h + y p = C 1 e-2 t + C 2 e 5 t-1 7 te-2 t . 1...
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- Spring '07