What is the solution for y^{''}-y^'-2y=3x+6 ?

The solution for y^{''}-y^'-2y=3x+6 is y=c_{1}e^{2x}+c_{2}e^{-x}-(3x)/2-9/4

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y^{''}-y^'-2y=3x+6

y^{^{''}} - y^{^{'}} - 2 y = 3 x + 6

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x}{2} - \frac{9}{4}

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 3 x + 6

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x}{2} - \frac{9}{4}

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x}{2} - \frac{9}{4}

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 4 e^{- t} cos (2 t)

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{( 1 + x ) ( 2 + x )}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 45 y = e^{5 x}

What is the solution for y^{''}-y^'-2y=3x+6 ?
The solution for y^{''}-y^'-2y=3x+6 is y=c_{1}e^{2x}+c_{2}e^{-x}-(3x)/2-9/4