What is the solution for (D^2+5D+6)y=(D+1)x ?

The solution for (D^2+5D+6)y=(D+1)x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x(D+1))/6-(5(D+1))/(36)

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(D^2+5D+6)y=(D+1)x

(D^{2} + 5 D + 6) y = (D + 1) x

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ( D + 1 )}{6} - \frac{5 ( D + 1 )}{36}

Solution steps

(D^{2} + 5 D + 6) y = (D + 1) x

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ( D + 1 )}{6} - \frac{5 ( D + 1 )}{36}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ( D + 1 )}{6} - \frac{5 ( D + 1 )}{36}

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)

y^{^{''}} - 4 y^{^{'}} = 8 x^{2} + 2 e^{3 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = e^{- 2 x} + 3

x^{^{''}} + 7 x^{^{'}} + 10 x = 20, x (0) = 5, x^{^{'}} (0) = 3

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 x^{2} + 1

What is the solution for (D^2+5D+6)y=(D+1)x ?
The solution for (D^2+5D+6)y=(D+1)x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+(x(D+1))/6-(5(D+1))/(36)