What is the solution for y^{''}+y^'+x=0 ?

The solution for y^{''}+y^'+x=0 is y=c_{1}+c_{2}e^{-x}-(x^2)/2+x

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y^{''}+y^'+x=0

y^{^{''}} + y^{^{'}} + x = 0

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

Solution steps

y^{''} (x) + y^{'} (x) + x = 0

Solve linear ODE:

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

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

What is the solution for y^{''}+y^'+x=0 ?
The solution for y^{''}+y^'+x=0 is y=c_{1}+c_{2}e^{-x}-(x^2)/2+x