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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

y = 2 x^{3} - 8 x

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t \to 0 lim (\frac{4}{t} - \frac{4}{t ^{2} + t})

\int \frac{cos ^{5} ( t )}{sin ( t )} d t

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