What is the solution for (D^2+D-12)y=x ?

The solution for (D^2+D-12)y=x is y=c_{1}e^{3x}+c_{2}e^{-4x}-x/(12)-1/144

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(D^2+D-12)y=x

(D^{2} + D - 12) y = x

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{12} - \frac{1}{144}

Solution steps

(D^{2} + D - 12) y = x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{12} - \frac{1}{144}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{12} - \frac{1}{144}

y^{^{''}} - 8 y^{^{'}} + 16 y = (x - 1) e^{4 x}

y^{^{''}} + y = t - (t - 4) H (t - 2)

y^{^{''}} - 5 y^{^{'}} - 14 y = e^{x} (x + 1)

y^{^{''}} + 4 y = e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

(D^{3} + D^{2} + D + 1) y = x e^{x}

What is the solution for (D^2+D-12)y=x ?
The solution for (D^2+D-12)y=x is y=c_{1}e^{3x}+c_{2}e^{-4x}-x/(12)-1/144