2.500   ODE No. 500

\[ (a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0 \] Mathematica : cpu = 0.908565 (sec), leaf count = 100


\[\left \{\left \{y(x)\to -\frac {\sqrt {-a b+a x^2-2 a c_1 x+a c_1{}^2+b^2-b x^2}}{\sqrt {b-a}}\right \},\left \{y(x)\to \frac {\sqrt {-a b+a x^2-2 a c_1 x+a c_1{}^2+b^2-b x^2}}{\sqrt {b-a}}\right \}\right \}\] Maple : cpu = 1.176 (sec), leaf count = 220


\[y \relax (x ) = \frac {\sqrt {\left (a -b \right ) b \left (x^{2}+a -b \right )}}{a -b}\]