What is the solution for (d^2+3d+2)y=1+3x+x^2 ?

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

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(d^2+3d+2)y=1+3x+x^2

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

x^{^{''}} + 3 x^{^{'}} - 4 x = - 4 t + 3

y^{^{''}} - 4 y^{^{'}} + 4 = sin (x)

y^{^{''}} + 2 y^{^{'}} = 4, y (0) = 3, y^{^{'}} (0) = 5

y^{^{''}} + y = t sin (t)

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

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