Answer to Question #199450 in Differential Equations for Raghav Sood

Question

Find the differential equation of the family of curves x²+y²+2ax+2by+c=0, where a, b, c are parameters.

Answer 1

$\displaystyle x^2+y^2+2ax+2by+c=0\\ 2x + 2yy' + 2a + 2by' = 0\\ y'(2b + 2y) = -(2a + 2x)\\ y' = -\frac{(a + x)}{(b + y)}$