What is the solution for y^{''}-2y^'-15y=480e^{-t} ?

The solution for y^{''}-2y^'-15y=480e^{-t} is y=c_{1}e^{5t}+c_{2}e^{-3t}-40e^{-t}

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y^{''}-2y^'-15y=480e^{-t}

y^{^{''}} - 2 y^{^{'}} - 15 y = 480 e^{- t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 40 e^{- t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 15 y = 480 e^{- t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 40 e^{- t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 40 e^{- t}

What is the solution for y^{''}-2y^'-15y=480e^{-t} ?
The solution for y^{''}-2y^'-15y=480e^{-t} is y=c_{1}e^{5t}+c_{2}e^{-3t}-40e^{-t}