What is the solution for (dy)/(dx)= x/(4y) ?

The solution for (dy)/(dx)= x/(4y) is y=(sqrt(c_{1)+x^2})/2 ,y=-(sqrt(c_{1)+x^2})/2

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(dy)/(dx)= x/(4y)

\frac{d y}{d x} = \frac{x}{4 y}

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

Solution steps

\frac{d y}{d x} = \frac{x}{4 y}

Solve separable ODE:

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

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

\frac{x ^{2} + 1}{x ^{2} - 1}

\int \frac{3}{x ^{2} - 1} d x

\int 3 x e^{\frac{2 x}{3}} d x

\frac{d}{d x} (4 - 7 x)

\frac{d y}{d x} = 100 x - x y

What is the solution for (dy)/(dx)= x/(4y) ?
The solution for (dy)/(dx)= x/(4y) is y=(sqrt(c_{1)+x^2})/2 ,y=-(sqrt(c_{1)+x^2})/2