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}

\frac{\partial}{\partial x} (x^{a} y^{b})

\frac{\partial}{\partial x} (\frac{( 2 x )}{y})

y^{^{''}} - 4 y = 6 e^{t}

5 cos (2 x), 5 - 5 cos (2 x), 0, \frac{π}{2}

\int \frac{20 x ^{3}}{4 + 5 x ^{4}} d x

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}