What is the solution for (dy)/(dx)=-x/(5y) ?

The solution for (dy)/(dx)=-x/(5y) is y=sqrt(-(x^2)/5+c_{1)},y=-sqrt(-(x^2)/5+c_{1)}

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(dy)/(dx)=-x/(5y)

\frac{d y}{d x} = - \frac{x}{5 y}

y = - \frac{x ^{2}}{5} + c_{1}, y = - - \frac{x ^{2}}{5} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{x}{5 y}

Solve separable ODE:

y = - \frac{x ^{2}}{5} + c_{1}, y = - - \frac{x ^{2}}{5} + c_{1}

y = - \frac{x ^{2}}{5} + c_{1}, y = - - \frac{x ^{2}}{5} + c_{1}

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

\frac{d N}{d t} = 2 N

(1 + 5 e^{2 x}) (y^{2} - 4) y^{^{'}} = e^{2 x} (y + 2)

\frac{d y}{d x} = \frac{x y}{1 + x ^{2}}

(e^{y} + 1) cos (x) d x + e^{y} sin (x) d y = 0

What is the solution for (dy)/(dx)=-x/(5y) ?
The solution for (dy)/(dx)=-x/(5y) is y=sqrt(-(x^2)/5+c_{1)},y=-sqrt(-(x^2)/5+c_{1)}