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

The solution for (dy)/(dx)+y=((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)+y=((1+y^2))/(2y)

\frac{d y}{d x} + y = \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} + y = \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

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