#### 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 = 0.977149 (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 = 1.035 (sec), leaf count = 220

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