What is the solution for y^{''}+9y=10e^{-t} ?

The solution for y^{''}+9y=10e^{-t} is y=c_{1}cos(3t)+c_{2}sin(3t)+e^{-t}

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y^{''}+9y=10e^{-t}

y^{^{''}} + 9 y = 10 e^{- t}

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

Solution steps

y^{''} (t) + 9 y = 10 e^{- t}

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} + 6 y = (x - 2) e^{x}

y^{^{''}} - 2 y^{^{'}} + 37 y = e^{x} cos (6 x)

y^{^{''}} + 3 y^{^{'}} - 4 y = cos (2 x)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = e^{x}

y^{^{''}} - y = 8

What is the solution for y^{''}+9y=10e^{-t} ?
The solution for y^{''}+9y=10e^{-t} is y=c_{1}cos(3t)+c_{2}sin(3t)+e^{-t}