What is the solution for y^{'''}+y^{''}=8x^2 ?

The solution for y^{'''}+y^{''}=8x^2 is y=c_{1}e^{-x}+c_{2}+c_{3}x+(2x^4)/3-(8x^3)/3+8x^2

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y^{'''}+y^{''}=8x^2

y^{^{'''}} + y^{^{''}} = 8 x^{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{4}}{3} - \frac{8 x ^{3}}{3} + 8 x^{2}

Solution steps

y^{'''} (x) + y^{''} (x) = 8 x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{4}}{3} - \frac{8 x ^{3}}{3} + 8 x^{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{4}}{3} - \frac{8 x ^{3}}{3} + 8 x^{2}

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What is the solution for y^{'''}+y^{''}=8x^2 ?
The solution for y^{'''}+y^{''}=8x^2 is y=c_{1}e^{-x}+c_{2}+c_{3}x+(2x^4)/3-(8x^3)/3+8x^2