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

The solution for (D^2+2D+2)y=x^2+x+1 is y=e^{-x}(c_{1}cos(x)+c_{2}sin(x))+(x^2)/2-x/2+1/2

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

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

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{2}

Solution steps

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

Solve linear ODE:

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{2}

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{2}

y^{^{''}} + y^{^{'}} = sin (3 x)

y^{^{''}} + y = 3 x^{2} + 4

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

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{6} cos (t)

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

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