What is the solution for y^{''}-2y^'-3y=12e^x-9 ?

The solution for y^{''}-2y^'-3y=12e^x-9 is y=c_{1}e^{3x}+c_{2}e^{-x}-3e^x+3

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y^{''}-2y^'-3y=12e^x-9

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 9

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

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 12 e^{x} - 9

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin (x)

y^{^{''}} + 16 y = cos (4 t)

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

y^{^{''}} + 4 y = 3 csc (2 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

What is the solution for y^{''}-2y^'-3y=12e^x-9 ?
The solution for y^{''}-2y^'-3y=12e^x-9 is y=c_{1}e^{3x}+c_{2}e^{-x}-3e^x+3