What is a solution to the differential equation dy/dx=sinx/y?

Oct 28, 2016

${y}^{2} = - 2 \cos x + {C}_{2}$

Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \sin \frac{x}{y}$

separate variables

$\int y \mathrm{dy} = \int \sin x \mathrm{dx}$

$\frac{1}{2} {y}^{2} = - \cos x + {C}_{1}$

$\implies {y}^{2} = - 2 \cos x + {C}_{2}$