What is the solution for (d^2-2d+1)*y=e^x*x^2 ?

The solution for (d^2-2d+1)*y=e^x*x^2 is y=c_{1}e^x+c_{2}xe^x+(e^xx^4)/(12)

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(d^2-2d+1)y=e^xx^2

(d^{2} - 2 d + 1) \cdot y = e^{x} \cdot x^{2}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = e^{x} - x + 16

(d^{2} + 4 d + 5) \cdot y = - 2 cos (x)

(d^{3} - 3 d + 2) \cdot y = 540 x^{3} \cdot e^{- x}

(d^{3} + 8) \cdot y = x^{4} + 2 x + 1 + 3 sin (x)

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

What is the solution for (d^2-2d+1)*y=e^x*x^2 ?
The solution for (d^2-2d+1)*y=e^x*x^2 is y=c_{1}e^x+c_{2}xe^x+(e^xx^4)/(12)