What is the solution for y^{'''}-y^'=4x^2+5x-2 ?

The solution for y^{'''}-y^'=4x^2+5x-2 is y=c_{1}+c_{2}e^{-x}+c_{3}e^x-(4x^3)/3-(5x^2)/2-6x

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y^{'''}-y^'=4x^2+5x-2

y^{^{'''}} - y^{^{'}} = 4 x^{2} + 5 x - 2

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 6 x

Solution steps

y^{'''} (x) - y^{'} (x) = 4 x^{2} + 5 x - 2

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 6 x

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} - 6 x

y^{^{''}} + 3 y^{^{'}} + 2 y = 1 + 4 x e^{- 3 x}

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = e^{t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + x, y (0) = 0, y^{^{'}} (0) = 4

y^{^{''}} - 2 y^{^{'}} + y = x^{3} e^{x}

y^{^{''}} + 2 y - 1 = 0

What is the solution for y^{'''}-y^'=4x^2+5x-2 ?
The solution for y^{'''}-y^'=4x^2+5x-2 is y=c_{1}+c_{2}e^{-x}+c_{3}e^x-(4x^3)/3-(5x^2)/2-6x