#### 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 = 0.721782 (sec), leaf count = 79

$\left \{\left \{y(x)\to -\sqrt {-2 a c_1 x+a c_1{}^2+b+2 c_1 x-c_1{}^2-x^2}\right \},\left \{y(x)\to \sqrt {-2 a c_1 x+a c_1{}^2+b+2 c_1 x-c_1{}^2-x^2}\right \}\right \}$ Maple : cpu = 0.925 (sec), leaf count = 195

$\left \{ y \left ( x \right ) =\sqrt {-a{x}^{2}+b},y \left ( x \right ) ={\frac {1}{a}\sqrt {a \left ( -2\,x\sqrt {-a \left ( b-{\it \_C1} \right ) \left ( a-1 \right ) }+ \left ( -{x}^{2}+b \right ) a-b+{\it \_C1} \right ) }},y \left ( x \right ) ={\frac {1}{a}\sqrt { \left ( 2\,x\sqrt {-a \left ( b-{\it \_C1} \right ) \left ( a-1 \right ) }+ \left ( -{x}^{2}+b \right ) a-b+{\it \_C1} \right ) a}},y \left ( x \right ) =-\sqrt {-a{x}^{2}+b},y \left ( x \right ) =-{\frac {1}{a}\sqrt {a \left ( -2\,x\sqrt {-a \left ( b-{\it \_C1} \right ) \left ( a-1 \right ) }+ \left ( -{x}^{2}+b \right ) a-b+{\it \_C1} \right ) }},y \left ( x \right ) =-{\frac {1}{a}\sqrt { \left ( 2\,x\sqrt {-a \left ( b-{\it \_C1} \right ) \left ( a-1 \right ) }+ \left ( -{x}^{2}+b \right ) a-b+{\it \_C1} \right ) a}} \right \}$