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

The solution for (D^2-6D+9)y=x^2e^{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) y = x^{2} 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}

y^{^{''}} + 2 y^{^{'}} + 10 = 0, y (0) = - 2, y^{^{'}} (0) = 0

4 y^{^{''}} + y = 10 cos (x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 e^{- 2} x

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

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

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