# Eliminate arbitrary constant and obtain differential equation $x^2-y^2= a(x^2+y^2)^2$

$(a)\;y'= \frac{x}{2y} \\ (b)\;3y=2y'x \\ (c)\;y'= \frac{x}{y} \\ (d)\;y'=\frac{z}{y}$

$2x-2yy'= a2(x^2+y^2(2x+2yy'))$
$x=yy'= 2a(x^2+y^2)(x+yy')$