What is the solution for (dy)/(dx)=-(2x)/(6y) ?

The solution for (dy)/(dx)=-(2x)/(6y) is y=sqrt(-(x^2)/3+c_{1)},y=-sqrt(-(x^2)/3+c_{1)}

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(dy)/(dx)=-(2x)/(6y)

\frac{d y}{d x} = - \frac{2 x}{6 y}

y = - \frac{x ^{2}}{3} + c_{1}, y = - - \frac{x ^{2}}{3} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{2 x}{6 y}

Solve separable ODE:

y = - \frac{x ^{2}}{3} + c_{1}, y = - - \frac{x ^{2}}{3} + c_{1}

y = - \frac{x ^{2}}{3} + c_{1}, y = - - \frac{x ^{2}}{3} + c_{1}

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

y^{^{'}} + y = y (sin (x) + 1)

\frac{d y}{d x} = 2 y tan (x)

(x^{2} + 1) sin (y) y^{^{'}} = - 2 x cos (y)

\frac{d y}{d t} = - 3 y

What is the solution for (dy)/(dx)=-(2x)/(6y) ?
The solution for (dy)/(dx)=-(2x)/(6y) is y=sqrt(-(x^2)/3+c_{1)},y=-sqrt(-(x^2)/3+c_{1)}