What is the solution for (d+d+d^2)y=5x^2 ?

The solution for (d+d+d^2)y=5x^2 is y=c_{1}+c_{2}e^{-2x}+(5x^3)/6-(5x^2)/4+(5x)/4

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(d+d+d^2)y=5x^2

(d + d + d^{2}) y = 5 x^{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{5 x ^{3}}{6} - \frac{5 x ^{2}}{4} + \frac{5 x}{4}

Solution steps

(d + d + d^{2}) y = 5 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{5 x ^{3}}{6} - \frac{5 x ^{2}}{4} + \frac{5 x}{4}

y = c_{1} + c_{2} e^{- 2 x} + \frac{5 x ^{3}}{6} - \frac{5 x ^{2}}{4} + \frac{5 x}{4}

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

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

(d^{2} + 1) y = x^{2} e^{3} x

4 y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- 3} x + 18 x + 15

(d^{5} - d) y = 12 e^{x} + 8 sin (x) - 2 x

What is the solution for (d+d+d^2)y=5x^2 ?
The solution for (d+d+d^2)y=5x^2 is y=c_{1}+c_{2}e^{-2x}+(5x^3)/6-(5x^2)/4+(5x)/4