What is the solution for y^{''}-2y^'-3y=4e^x-6 ?

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

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y^{''}-2y^'-3y=4e^x-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 6

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

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 4 e^{x} - 6

Solve linear ODE:

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

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

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

y^{^{''}} + 36 y = 24 cos (6 x) - 12 sin (6 x)

y^{^{''}} - 4 y = 4 t - 4, y (0) = 2, y^{^{'}} (0) = 9

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 3

y^{^{''}} + 4 y = x cos (x)

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