Answer to Question #339745 in Differential Equations for Mayo

Question

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

Answer 1

Question

$\frac {dy} {dx}=-\frac {x} {2y}$

Solution.

We have:

$\frac {dy} {dx}=-\frac {x} {2y}$

$2y\,dy=-x\,dx$

$\int {2y} \ dy=\int {-x}\ dx$

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

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

$y=\pm \sqrt{-\frac {x^2} {2} + C}$

$y^2=-\frac {x^2} {2} + C$ is the general integral in an implicit form.