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}

2 y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} - 8 y = e^{- t}

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

490 y^{^{''}} + 20 y = 8 cos (6 t)

\frac{d ^{2} y}{d x ^{2}} - 4 y = \frac{e ^{2 x}}{x}

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

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