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# Math - Differential Equations?

Solve the initial value problem:

y" - 4y = t(e^t)

y(0) = 0;

y'(0) = 1;

Thanks!

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### 2 Answers

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- Anonymous1 decade agoFavorite Answer
particular solution yp = (At + B)e^t ----> (yp)" = ... , plug in the ODE ---> A = -1/3 , B = -2/3

general solution

y = Ce^2t + De^2t -(1/3)(t+2)e^t , and use 2 conditions y(0) = 0; y'(0) = 1; to find C ,D

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