Plugging in our first initial condition we get 0 c 1

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Plugging in our first initial condition we get 0 = c 1 + c 2 Next we compute y 0 ( x ) to get y 0 ( x ) = something x 7 / 2 - 2 c 1 e - 2 x + c 2 e - 2 x - 2 c 2 xe - 2 x and plugging in our second initial condition gives 1 = - 2 c 1 - c 2 . Since c 2 = - c 1 this gives 1 = - 2 c 1 + c 1 = - c 1 . So c 1 = - 1 and hence c 1 = 1 . Then the solution to the IVP is y ( x ) = 4 63 x 9 / 2 e - 2 x - e - 2 x + xe - 2 x .
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