What is the solution for (D^2-D-2)y=6e-t^2 ?

The solution for (D^2-D-2)y=6e-t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}+(t^2)/2-t/2-(12e-3)/4

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(D^2-D-2)y=6e-t^2

(D^{2} - D - 2) y = 6 e - t^{2}

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

Solution steps

(D^{2} - D - 2) y = 6 e - t^{2}

Solve linear ODE:

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

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

What is the solution for (D^2-D-2)y=6e-t^2 ?
The solution for (D^2-D-2)y=6e-t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}+(t^2)/2-t/2-(12e-3)/4