What is the solution for (d^2-4d+4)y=x^3 ?

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

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

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{4} + \frac{9 x}{8} + \frac{3}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{4} + \frac{9 x}{8} + \frac{3}{4}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{4} + \frac{9 x}{8} + \frac{3}{4}

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

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

(d^{2} - 2 d + 1) y = x^{2} e^{x}

y^{^{''}} + 3 y^{^{'}} = - 48 x^{2} e^{3} x

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

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