What is the solution for y^{''}+y^'-2y=9e^x-2 ?

The solution for y^{''}+y^'-2y=9e^x-2 is y=c_{1}e^x+c_{2}e^{-2x}+3xe^x+1

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y^{''}+y^'-2y=9e^x-2

y^{^{''}} + y^{^{'}} - 2 y = 9 e^{x} - 2

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

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = 9 e^{x} - 2

Solve linear ODE:

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

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

\frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 2 x = 2 e^{- 3 t}

y^{^{''}} - y^{^{'}} - 6 y = 19 sin (3 x)

x^{^{''}} - 3 x^{^{'}} + 2 x = t^{2} e^{t}

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

y^{^{''}} + 36 y = 60 sin (6 t)

What is the solution for y^{''}+y^'-2y=9e^x-2 ?
The solution for y^{''}+y^'-2y=9e^x-2 is y=c_{1}e^x+c_{2}e^{-2x}+3xe^x+1