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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d t} = - \frac{1}{50} (y - 23)

y^{^{'}} sec (x) = 6 y^{2}, y (\frac{9 π}{2}) = \frac{1}{7}

(x + 1) d x - y d y = 0

\frac{d y}{d t} + t y = y, y (1) = 3

y^{^{'}} = e^{- y} \frac{x ^{5}}{7}

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