What is the solution for y^{''}+2y^'-3y=32(3x+1)e^{-3x} ?

The solution for y^{''}+2y^'-3y=32(3x+1)e^{-3x} is y=c_{1}e^x+c_{2}e^{-3x}-12x^2e^{-3x}-14e^{-3x}x

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y^{''}+2y^'-3y=32(3x+1)e^{-3x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 32 (3 x + 1) e^{- 3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} - 12 x^{2} e^{- 3 x} - 14 e^{- 3 x} x

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 32 (3 x + 1) e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} - 12 x^{2} e^{- 3 x} - 14 e^{- 3 x} x

y = c_{1} e^{x} + c_{2} e^{- 3 x} - 12 x^{2} e^{- 3 x} - 14 e^{- 3 x} x

y^{^{''}} + y^{^{'}} = cos (2 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 1 = e^{x}

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

y^{^{''}} + 9 y = 5 csc^{2} (3 x)

y^{^{''}} - y - 12 y = e^{4 x}

What is the solution for y^{''}+2y^'-3y=32(3x+1)e^{-3x} ?
The solution for y^{''}+2y^'-3y=32(3x+1)e^{-3x} is y=c_{1}e^x+c_{2}e^{-3x}-12x^2e^{-3x}-14e^{-3x}x