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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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