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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 5 H (t)

y^{^{''}} + 3 \cdot y^{^{'}} + 2 \cdot y = x

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

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 1, x (0) = 0

y^{^{''}} - y^{^{'}} + y = 14 sin (t)

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