What is the solution for y^{''}+4y^'+3y=64e^t,y(0)=4,y^'(0)=7 ?

The solution for y^{''}+4y^'+3y=64e^t,y(0)=4,y^'(0)=7 is y=(-5/2-4)e^{-t}+5/2 e^{-3t}+8e^t

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y^{''}+4y^'+3y=64e^t,y(0)=4,y^'(0)=7

y^{^{''}} + 4 y^{^{'}} + 3 y = 64 e^{t}, y (0) = 4, y^{^{'}} (0) = 7

y = (- \frac{5}{2} - 4) e^{- t} + \frac{5}{2} e^{- 3 t} + 8 e^{t}

Solution steps

y^{''} (t) + 4 y^{'} (t) + 3 y = 64 e^{t}

Solve linear ODE:

y = (- \frac{5}{2} - 4) e^{- t} + \frac{5}{2} e^{- 3 t} + 8 e^{t}

y = (- \frac{5}{2} - 4) e^{- t} + \frac{5}{2} e^{- 3 t} + 8 e^{t}

What is the solution for y^{''}+4y^'+3y=64e^t,y(0)=4,y^'(0)=7 ?
The solution for y^{''}+4y^'+3y=64e^t,y(0)=4,y^'(0)=7 is y=(-5/2-4)e^{-t}+5/2 e^{-3t}+8e^t