What is the solution for (D^2+5D+4)Y=x^2+7x+9 ?

The solution for (D^2+5D+4)Y=x^2+7x+9 is Y(x)=c_{1}e^{-x}+c_{2}e^{-4x}+(x^2)/4+(9x)/8+23/32

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(D^2+5D+4)Y=x^2+7x+9

(D^{2} + 5 D + 4) Y = x^{2} + 7 x + 9

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

Solution steps

(D^{2} + 5 D + 4) Y (x) = x^{2} + 7 x + 9

Solve linear ODE:

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

What is the solution for (D^2+5D+4)Y=x^2+7x+9 ?
The solution for (D^2+5D+4)Y=x^2+7x+9 is Y(x)=c_{1}e^{-x}+c_{2}e^{-4x}+(x^2)/4+(9x)/8+23/32