What is the solution for (D^2-4)y=4x-3e^x ?

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

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(D^2-4)y=4x-3e^x

(D^{2} - 4) y = 4 x - 3 e^{x}

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

Solution steps

(D^{2} - 4) y = 4 x - 3 e^{x}

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{''}} - y^{^{'}} + 1 = 0

y^{^{''}} + 9 y = sin (2 x), y (0) = - 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + y = e^{3} + e^{2 x}

y^{^{''}} + y^{^{'}} + 12 y = 20 cos (3 t)

y^{^{''}} - 9 y = sin (x)

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