Chrystal's equation
In mathematics, Chrystal's equation is a first order nonlinear ordinary differential equation, named after the mathematician George Chrystal, who discussed the singular solution of this equation in 1896. The equation reads as ( d y d x ) 2 + A x d y d x + B y + C x 2 = 0 {\displaystyle \left({\frac {dy}{dx}}\right)^{2}+Ax{\frac {dy}{dx}}+By+Cx^{2}=0} where A , B , C {\displaystyle A,\ B,\ C} are constants, which upon solving for d y / d x {\displaystyle dy/dx} , gives d y d x = − A 2 x ± 1 2 ( A 2 x 2 − 4 B y − 4 C x 2 ) 1 / 2 .