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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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