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

The solution for y^{'''}+y^{''}-y^'-y=2e^{-x} is y=c_{1}e^x+c_{2}e^{-x}+c_{3}xe^{-x}-(e^{-x}x^2)/2

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} - 28 y = 528 e^{- t}

y^{^{''}} + y^{^{'}} + y = e^{3 x} + 6 e^{x} - 3 e^{- 2 x} + 5

d (x) = 5 (x - 3)^{2} + 1

v^{^{''}} + 2 v^{^{'}} + v = e^{- 2 t}

y^{^{''}} + y^{^{'}} - 2 y = 4

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