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

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

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

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

y = \frac{x ^{2}}{2} + c_{1}, y = - \frac{x ^{2}}{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{2}}{2} + c_{1}, y = - \frac{x ^{2}}{2} + c_{1}

y = \frac{x ^{2}}{2} + c_{1}, y = - \frac{x ^{2}}{2} + c_{1}

d er i v a t i v e y = \frac{1}{4 x ^{3}} - \frac{6}{5 x ^{4}}

t a y l or x^{- 2}

\int \frac{( x ^{4} )}{x ^{2} + 4} d x

\frac{d y}{d x} = \frac{- y ^{2}}{1 + y ^{2}} e^{- x}, y (0) = 1

x \to - 2 lim (h (x))

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