What is the solution for (D^2-4D+4)(y)=6x^2e^{2x} ?

The solution for (D^2-4D+4)(y)=6x^2e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+(e^{2x}x^4)/2

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(D^2-4D+4)(y)=6x^2e^{2x}

(D^{2} - 4 D + 4) (y) = 6 x^{2} e^{2 x}

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

Solution steps

(D^{2} - 4 D + 4) y = 6 x^{2} e^{2 x}

Solve linear ODE:

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

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

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t}

y^{^{''}} + y = sec^{2} (x), y (0) = 2, y^{^{'}} (0) = 1

D (D - 3) y = 3 t + \frac{t}{2}

8 y^{^{''}} - 6 y^{^{'}} + y = 6 cosh (x)

y^{^{''}} - 100 y = 15

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