What is the solution for y^{''}+4y+5y=e^{-t} ?

The solution for y^{''}+4y+5y=e^{-t} is y=c_{1}cos(3t)+c_{2}sin(3t)+1/10 e^{-t}

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y^{''}+4y+5y=e^{-t}

y^{^{''}} + 4 y + 5 y = e^{- t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{- t}

Solution steps

y^{''} (t) + 4 y + 5 y = e^{- t}

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{- t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{- t}

What is the solution for y^{''}+4y+5y=e^{-t} ?
The solution for y^{''}+4y+5y=e^{-t} is y=c_{1}cos(3t)+c_{2}sin(3t)+1/10 e^{-t}