What is the solution for (d^2-6d+9)*y=x^2*e^{2x} ?

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

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(d^2-6d+9)y=x^2e^{2x}

(d^{2} - 6 d + 9) \cdot y = x^{2} \cdot e^{2 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + e^{2 x} x^{2} + 4 x e^{2 x} + 6 e^{2 x}

Solution steps

(d^{2} - 6 d + 9) y = x^{2} e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + e^{2 x} x^{2} + 4 x e^{2 x} + 6 e^{2 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + e^{2 x} x^{2} + 4 x e^{2 x} + 6 e^{2 x}

0.2 y^{^{''}} + 1.2 y^{^{'}} + 2 y = 5 cos (x)

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

y^{^{''}} + 9 y = 27 x^{2}

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

d^{2} (d^{2} + 4) y = 96 x^{2} + sin^{2} (x) - k

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