2.501   ODE No. 501

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

\[ y'(x)^2 \left (a y(x)^2+b x+c\right )-b y(x) y'(x)+d y(x)^2=0 \] Mathematica : cpu = 300.489 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 4.984 (sec), leaf count = 215

\[ \left \{ [x \left ( {\it \_T} \right ) =-{\frac {1}{4\,bd} \left ( \sqrt {{{\it \_T}}^{2}a+d} \left ( \ln \left ( {\frac {1}{{\it \_T}} \left ( \sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}+d \right ) } \right ) \right ) ^{2}{b}^{2}+ \left ( \left ( 2\,\ln \left ( 2 \right ) {b}^{2}+4\,\sqrt {d}{\it \_C1}\,b \right ) \sqrt {{{\it \_T}}^{2}a+d}-2\,\sqrt {d}{b}^{2} \right ) \ln \left ( {\frac {1}{{\it \_T}} \left ( \sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}+d \right ) } \right ) + \left ( 4\,\sqrt {d}\ln \left ( 2 \right ) {\it \_C1}\,b+ \left ( \ln \left ( 2 \right ) \right ) ^{2}{b}^{2}+4\,d \left ( {{\it \_C1}}^{2}+c \right ) \right ) \sqrt {{{\it \_T}}^{2}a+d}-2\,\sqrt {d}\ln \left ( 2 \right ) {b}^{2}-4\,{\it \_C1}\,bd \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}a+d}}}},y \left ( {\it \_T} \right ) ={\frac {{\it \_T}}{2} \left ( 2\,{\it \_C1}\,\sqrt {d}+b\ln \left ( {\frac {1}{{\it \_T}} \left ( \sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}+d \right ) } \right ) +b\ln \left ( 2 \right ) \right ) {\frac {1}{\sqrt {d}}}{\frac {1}{\sqrt {{{\it \_T}}^{2}a+d}}}}] \right \} \]