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

The solution for y^{'''}+y^{''}=x-e^{-x} is y=c_{1}e^{-x}+c_{2}+c_{3}x+(x^3)/6-(x^2)/2-e^{-x}x

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

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

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{x ^{3}}{6} - \frac{x ^{2}}{2} - e^{- x} x

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{x ^{3}}{6} - \frac{x ^{2}}{2} - e^{- x} x

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{x ^{3}}{6} - \frac{x ^{2}}{2} - e^{- x} x

\int x sin (\frac{1}{11} x) d x

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

y^{^{''}} + 16 y^{^{'}} + 65 y = 0

\frac{d}{d x} (x^{2} - 25 ln (x^{2}))

f (x) = \frac{x}{x ^{2} - 6}

What is the solution for y^{'''}+y^{''}=x-e^{-x} ?
The solution for y^{'''}+y^{''}=x-e^{-x} is y=c_{1}e^{-x}+c_{2}+c_{3}x+(x^3)/6-(x^2)/2-e^{-x}x