What is the solution for y^{'''}+y^{''}=x+1 ?

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

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y^{'''}+y^{''}=x+1

y^{^{'''}} + y^{^{''}} = x + 1

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

Solution steps

y^{'''} (x) + y^{''} (x) = x + 1

Solve linear ODE:

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

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

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