What is the solution for (d^3+2d^2+d)y=+x^2+x ?

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

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(d^3+2d^2+d)y=+x^2+x

(d^{3} + 2 d^{2} + d) y = + x^{2} + x

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

Solution steps

(d^{3} + 2 d^{2} + d) y = x^{2} + x

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 6 y = 3 x - 1

(d^{2} + 3 d + 2) \cdot y = e^{e^{x}}

(d^{2} + 9) y = sin^{2} (x)

(d^{2} - 1) y = x^{2} + cos^{2} (x)

(d^{2} + d - 6) y = e^{2} x \cdot sin^{3} (x)

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