2.491   ODE No. 491

\[ (a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0 \] Mathematica : cpu = 0.716191 (sec), leaf count = 79


\[\left \{\left \{y(x)\to -\sqrt {-2 a c_1 x+a c_1{}^2+b-x^2+2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to \sqrt {-2 a c_1 x+a c_1{}^2+b-x^2+2 c_1 x-c_1{}^2}\right \}\right \}\] Maple : cpu = 0.8 (sec), leaf count = 195


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