What is the solution for y^{''}-y=4e-x^1-e-2x ?

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

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y^{''}-y=4e-x^1-e-2x

y^{^{''}} - y = 4 e - x^{1} - e - 2 x

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

Solution steps

y^{''} (x) - y = 4 e - x^{1} - e - 2 x

Solve linear ODE:

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

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

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

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

y^{^{''}} + 40 y^{^{'}} + 625 y = 100 cos (10 t)

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

y^{^{''}} + 4 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

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