What is the solution for (D^2-D-2)y=36xe^{2x} ?

The solution for (D^2-D-2)y=36xe^{2x} is y=c_{1}e^{2x}+c_{2}e^{-x}+6x^2e^{2x}-4e^{2x}x

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(D^2-D-2)y=36xe^{2x}

(D^{2} - D - 2) y = 36 x e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + 6 x^{2} e^{2 x} - 4 e^{2 x} x

Solution steps

(D^{2} - D - 2) y = 36 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + 6 x^{2} e^{2 x} - 4 e^{2 x} x

y = c_{1} e^{2 x} + c_{2} e^{- x} + 6 x^{2} e^{2 x} - 4 e^{2 x} x

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 sin (x) + (12 x - 10) e^{4 x}

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} - 4 y = 2 sin (x)

y^{^{''}} + 16 y = - 8 sin (4 x) + 17 e^{x}

y^{^{''}} + 2 y^{^{'}} + 17 y = - 44 - 85 x

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

What is the solution for (D^2-D-2)y=36xe^{2x} ?
The solution for (D^2-D-2)y=36xe^{2x} is y=c_{1}e^{2x}+c_{2}e^{-x}+6x^2e^{2x}-4e^{2x}x