What is the solution for (d^2+5d+6)*y=x^2 ?

The solution for (d^2+5d+6)*y=x^2 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x^2)/6-(5x)/(18)+19/108

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(d^2+5d+6)*y=x^2

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

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

Solution steps

(d^{2} + 5 d + 6) y = x^{2}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

What is the solution for (d^2+5d+6)*y=x^2 ?
The solution for (d^2+5d+6)*y=x^2 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x^2)/6-(5x)/(18)+19/108