What is the solution for (D^2-D-2)y=3e^{2x} ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 18 y = (t + 1) e^{t}

y^{^{''}} + y = H (t)

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x) + sin (2 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 104 sin (3 x)

x^{^{''}} + 2 x^{^{'}} + 5 x = 4 t^{2}

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