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}

(d^{3} + 8) y = x^{4} + 2 x + 1

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

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)

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

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