What is the solution for (dy)/(dx)= x/(6y) ?

The solution for (dy)/(dx)= x/(6y) is y=sqrt((x^2)/6+c_{1)},y=-sqrt((x^2)/6+c_{1)}

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(dy)/(dx)= x/(6y)

\frac{d y}{d x} = \frac{x}{6 y}

y = \frac{x ^{2}}{6} + c_{1}, y = - \frac{x ^{2}}{6} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{6 y}

Solve separable ODE:

y = \frac{x ^{2}}{6} + c_{1}, y = - \frac{x ^{2}}{6} + c_{1}

y = \frac{x ^{2}}{6} + c_{1}, y = - \frac{x ^{2}}{6} + c_{1}

\frac{\partial}{\partial y} (x^{4} - x^{2} - 2 x y + y^{2} + 1)

\frac{d}{d x} (e^{4 e^{x}})

\int \frac{1}{x x ^{4} + 1} d x

\int \frac{2 x}{16 x ^{4} - 9} d x

2 x e^{x} cos (x)

What is the solution for (dy)/(dx)= x/(6y) ?
The solution for (dy)/(dx)= x/(6y) is y=sqrt((x^2)/6+c_{1)},y=-sqrt((x^2)/6+c_{1)}