What is the solution for y^{''}-2y^'-15y=384e^{-t} ?

The solution for y^{''}-2y^'-15y=384e^{-t} is y=c_{1}e^{5t}+c_{2}e^{-3t}-32e^{-t}

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y^{''}-2y^'-15y=384e^{-t}

y^{^{''}} - 2 y^{^{'}} - 15 y = 384 e^{- t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 32 e^{- t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 15 y = 384 e^{- t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 32 e^{- t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - 32 e^{- t}

y^{^{''}} + 4 y = - 1, y (\frac{π}{8}) = \frac{3}{4}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} + 5 y^{^{'}} + 4 y = 12

y^{^{''}} - 22 y^{^{'}} + 121 y = \frac{e ^{- 11 x}}{1 + x ^{2}}

x^{^{''}} - x = sin (t)

y^{^{''}} + 5 y^{^{'}} - 6 y = 10 e^{2 x}

What is the solution for y^{''}-2y^'-15y=384e^{-t} ?
The solution for y^{''}-2y^'-15y=384e^{-t} is y=c_{1}e^{5t}+c_{2}e^{-3t}-32e^{-t}