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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

f (x) = \frac{1}{4 ( 1 + x ^{2} )}, g (x) = \frac{1}{8} x^{2}

\frac{d}{d x} (\frac{2 y}{x ^{2} + y ^{2}})

x \to 45 lim (\frac{x ^{2}}{9} - \frac{5}{x})

\frac{d}{d x} (sin^{5} (2 x))

\frac{\partial}{\partial x} (x e^{x^{2}})

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