2.1780   ODE No. 1780

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

\[ -a x-b+y(x)^2 y''(x)+y(x) y'(x)^2=0 \] Mathematica : cpu = 20.3733 (sec), leaf count = 0 , could not solve

DSolve[-b - a*x + y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 2.125 (sec), leaf count = 156

\[\left \{-c_{2}+\frac {b \ln \left (a x +b \right )}{a}-\frac {\sqrt {3}\, \left (\int _{}^{\frac {y \left (x \right )}{a x +b}}-\frac {2 \left (-\frac {3 \left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} b \tan \left (\RootOf \left (6 b^{2} \left (\int \frac {\left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2}}{\textit {\_g}^{3} a^{2}-1}d \textit {\_g} \right )+6 c_{1}-2 \sqrt {3}\, \textit {\_Z} +\ln \left (\frac {\tan ^{2}\left (\textit {\_Z} \right )+1}{\tan ^{2}\left (\textit {\_Z} \right )+2 \sqrt {3}\, \tan \left (\textit {\_Z} \right )+3}\right )\right )\right )}{2}+\sqrt {3}\, \left (a -\frac {\left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} b}{2}\right )\right ) \textit {\_g}^{2} b}{\textit {\_g}^{3} a^{2}-1}d \textit {\_g} \right )}{6} = 0\right \}\]