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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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