2.500   ODE No. 500

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ (a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0 \] Mathematica : cpu = 1.3044 (sec), leaf count = 100

\[\left \{\left \{y(x)\to -\frac {\sqrt {-a b-2 a c_1 x+a c_1^2+a x^2+b^2-b x^2}}{\sqrt {b-a}}\right \},\left \{y(x)\to \frac {\sqrt {-a b-2 a c_1 x+a c_1^2+a x^2+b^2-b x^2}}{\sqrt {b-a}}\right \}\right \}\]

Maple : cpu = 0.93 (sec), leaf count = 260

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