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{d}{d x} (x^{2} \cdot y)

\int_{0}^{1} \frac{4}{x ( x + 1 )} d x

y = 4 (x + 1), y = 5 (x + 1), x = 2

\frac{d}{d x} (3 x^{2} y^{2})

\frac{d}{d x} (x (1 - x^{2})^{\frac{1}{2}})

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