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

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

2 y^{^{''}} - 7 y^{^{'}} + 5 y = 11 - 7 x - 16 x^{2} + 5 x^{3}

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

y^{^{''}} + y^{^{'}} = 20

4 y^{^{''}} + 36 y = csc (3 x) 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