What is the solution for y^{''}-2y^'-3y=8e^x-6 ?

The solution for y^{''}-2y^'-3y=8e^x-6 is y=c_{1}e^{3x}+c_{2}e^{-x}-2e^x+2

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y^{''}-2y^'-3y=8e^x-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{x} - 6

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

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 8 e^{x} - 6

Solve linear ODE:

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

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

y^{^{''}} + 7 y^{^{'}} + 12 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{7 t}

y^{^{''}} + 3 y^{^{'}} - 18 y = - 66 t + 36 t^{2}

y^{^{''}} + 3 y^{^{'}} + 2 y = 4 x^{2}

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 e^{- 2 t}

What is the solution for y^{''}-2y^'-3y=8e^x-6 ?
The solution for y^{''}-2y^'-3y=8e^x-6 is y=c_{1}e^{3x}+c_{2}e^{-x}-2e^x+2