What is the solution for y^{''}-y^'-2y=6x+6e^{-x} ?

The solution for y^{''}-y^'-2y=6x+6e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}-3x+3/2-2xe^{-x}

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y^{''}-y^'-2y=6x+6e^{-x}

y^{^{''}} - y^{^{'}} - 2 y = 6 x + 6 e^{- x}

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

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 6 x + 6 e^{- x}

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} )}

D (x) = - 6 x + 4200

y^{^{''}} + 4 y = - 2, y (\frac{π}{8}) = \frac{1}{2}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} - 4 y^{^{'}} - 5 y = e^{x} + 2 x

y^{^{''''}} + 2 y^{^{''}} + y = 5 + cos (2 t)

What is the solution for y^{''}-y^'-2y=6x+6e^{-x} ?
The solution for y^{''}-y^'-2y=6x+6e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}-3x+3/2-2xe^{-x}