What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)+1=0 ?

The solution for (d^2y)/(dx^2)+2(dy)/(dx)+1=0 is y=c_{1}+c_{2}e^{-2x}-x/2

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(d^2y)/(dx^2)+2(dy)/(dx)+1=0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 1 = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 1 = 0

Solve linear ODE:

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

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

y^{^{''}} - 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 2

2 y^{^{''}} - y^{^{'}} - 3 y = 3 x e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = \frac{1}{e ^{x} sin ( x )}

y^{^{''}} - 9 y^{^{'}} + 20 = 0

y^{^{''}} - y^{^{'}} = e^{- 3 t}

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)+1=0 ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)+1=0 is y=c_{1}+c_{2}e^{-2x}-x/2