What is the solution for y^{''}+3y^'+2y=e^{-5x}(33-36x) ?

The solution for y^{''}+3y^'+2y=e^{-5x}(33-36x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-3xe^{-5x}+e^{-5x}

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y^{''}+3y^'+2y=e^{-5x}(33-36x)

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 5 x} (33 - 36 x)

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

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = e^{- 5 x} (33 - 36 x)

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{3} + x

y^{^{''}} - y^{^{'}} = 2 x - 3

y^{^{''}} - y^{^{'}} = 2 x + 4

y^{^{''}} + 2 y^{^{'}} + 5 = 0

y^{^{''}} + 2 y^{^{'}} + 4 y = 5 x^{4} + 3 x^{2} - x

What is the solution for y^{''}+3y^'+2y=e^{-5x}(33-36x) ?
The solution for y^{''}+3y^'+2y=e^{-5x}(33-36x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-3xe^{-5x}+e^{-5x}