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 = 1.05828 (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 = 0.978 (sec), leaf count = 220

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