What is the solution for y^{''}+36y=e^{-t} ?

The solution for y^{''}+36y=e^{-t} is y=c_{1}cos(6t)+c_{2}sin(6t)+1/37 e^{-t}

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y^{''}+36y=e^{-t}

y^{^{''}} + 36 y = e^{- t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{37} e^{- t}

Solution steps

y^{''} (t) + 36 y = e^{- t}

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{37} e^{- t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{37} e^{- t}

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What is the solution for y^{''}+36y=e^{-t} ?
The solution for y^{''}+36y=e^{-t} is y=c_{1}cos(6t)+c_{2}sin(6t)+1/37 e^{-t}