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}-24/5 e^{-t/2}

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

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

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{24}{5} e^{- \frac{t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{24}{5} e^{- \frac{t}{2}}

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{24}{5} e^{- \frac{t}{2}}

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}-24/5 e^{-t/2}