What is the solution for (d^2-4d+4)y=8x^2e^2x ?

The solution for (d^2-4d+4)y=8x^2e^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}+2e^2x^3+6e^2x^2+9e^2x+6e^2

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(d^2-4d+4)y=8x^2e^2x

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 2 e^{2} x^{3} + 6 e^{2} x^{2} + 9 e^{2} x + 6 e^{2}

Solution steps

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 2 e^{2} x^{3} + 6 e^{2} x^{2} + 9 e^{2} x + 6 e^{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 2 e^{2} x^{3} + 6 e^{2} x^{2} + 9 e^{2} x + 6 e^{2}

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

(d^{3} - 2 d^{2} - 5 d + 6) \cdot y = 4 e^{- x} - x \cdot e^{2 x}

(d^{3} + 8) y = x^{2} + 2 x + 1

(d^{2} + 4 d + 5) y = x^{3}

(d^{3} - 8) y = x^{3}

What is the solution for (d^2-4d+4)y=8x^2e^2x ?
The solution for (d^2-4d+4)y=8x^2e^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}+2e^2x^3+6e^2x^2+9e^2x+6e^2