Home » Blog » Integrate the differential equation y′ = (-x)/y Integrate the differential equation y′ = (-x)/y by RoRi February 21, 2016 Integrate the differential equation We separate the variables and integrate, Related
![\[ y' = -\frac{x}{y}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-e14a9f1cd0e73eed6b4f507452ff9cb0_l3.png "Rendered by QuickLaTeX.com")
![\begin{align*} y' &= -\frac{x}{y} & \implies && yy' &= -x \\ && \implies && \int y \, dy &= -\int x \, dx \\[9pt] && \implies && \frac{1}{2}y^2 &= -\frac{1}{2}x^2 + C \\[9pt] && \implies && x^2 + y^2 &= C. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-1a02f920e489e88a400293728517f403_l3.png "Rendered by QuickLaTeX.com")