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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} - 19 y^{^{'}} + 90 y = 0

y^{^{''}} + 5 y^{^{'}} + \frac{29}{4} y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{7}{2}

y^{^{''''}} - 2 y^{^{''}} = 0

- 10 y^{^{''}} + y = 0

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