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

The solution for (D^2+5D+6)y=x^2+2x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x^2)/6+x/(18)-11/108

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(D^2+5D+6)y=x^2+2x

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

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

What is the solution for (D^2+5D+6)y=x^2+2x ?
The solution for (D^2+5D+6)y=x^2+2x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x^2)/6+x/(18)-11/108