What is the solution for y^{''}-2y^'-3y=8ex-12 ?

The solution for y^{''}-2y^'-3y=8ex-12 is y=c_{1}e^{3x}+c_{2}e^{-x}-(8ex)/3+(16e+36)/9

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y^{''}-2y^'-3y=8ex-12

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e x - 12

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{8 e x}{3} + \frac{16 e + 36}{9}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 8 e x - 12

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{8 e x}{3} + \frac{16 e + 36}{9}

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{8 e x}{3} + \frac{16 e + 36}{9}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 18

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

y^{^{''}} + 49 y = sec (7 x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x) + x e^{3 x}

y^{^{''}} - y^{^{'}} - 2 y = 10 sin (2 x)

What is the solution for y^{''}-2y^'-3y=8ex-12 ?
The solution for y^{''}-2y^'-3y=8ex-12 is y=c_{1}e^{3x}+c_{2}e^{-x}-(8ex)/3+(16e+36)/9