What is the solution for y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7 ?

The solution for y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7 is y=-e^{-3t}+2e^{-3t}t+2e^t

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y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7

y^{^{''}} + 6 y^{^{'}} + 9 y = 32 e^{t}, y (0) = 1, y^{^{'}} (0) = 7

y = - e^{- 3 t} + 2 e^{- 3 t} t + 2 e^{t}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 32 e^{t}

Solve linear ODE:

y = - e^{- 3 t} + 2 e^{- 3 t} t + 2 e^{t}

y = - e^{- 3 t} + 2 e^{- 3 t} t + 2 e^{t}

What is the solution for y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7 ?
The solution for y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7 is y=-e^{-3t}+2e^{-3t}t+2e^t