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

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

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

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

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

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

y^{^{'''}} + 6 y^{^{''}} = x^{2}

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

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

y^{^{''}} + y^{^{'}} = t^{2} + 2 t

y^{^{''}} + 9 y = 10, e^{- t} y (0) y^{^{'}} (0) = 0

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