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

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

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y^{'''}+y^{''}-y^'-y=4e^x

y^{^{'''}} + y^{^{''}} - y^{^{'}} - y = 4 e^{x}

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

Solution steps

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

Solve linear ODE:

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

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

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\frac{d}{d x} (2 e^{(x - 5)})

\int \frac{( x ^{2} + 2 )}{x + 1} d x

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