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}

\int \frac{3}{3 + e ^{x}} d x

y^{^{''}} + y^{^{'}} - 30 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

(2 x + 1)^{^{'}}

y^{^{'}} = (y + 2 x)^{2}, y (0) = 3

4 x^{4} + 3 x^{3} + 2 x^{2} + x + 11

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