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 = 0.492036 (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 = 0.654 (sec), leaf count = 160

\[ \left \{ {\frac {b\ln \left ( ax+b \right ) }{a}}-\int ^{{\frac {y \left ( x \right ) }{ax+b}}}\!-{\frac {{{\it \_g}}^{2}b\sqrt {3}}{6\,{{\it \_g}}^{3}{a}^{2}-6} \left ( -3\,\tan \left ( {\it RootOf} \left ( 6\,{b}^{2}\int \!{\frac {{{\it \_g}}^{2}}{{{\it \_g}}^{3}{a}^{2}-1} \left ( -{\frac {a}{{b}^{3}{{\it \_g}}^{3}}} \right ) ^{2/3}}\,{\rm d}{\it \_g}-2\,{\it \_Z}\,\sqrt {3}+\ln \left ( {\frac { \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1}{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+2\,\sqrt {3}\tan \left ( {\it \_Z} \right ) +3}} \right ) +6\,{\it \_C1} \right ) \right ) b\sqrt [3]{-{\frac {a}{{b}^{3}{{\it \_g}}^{3}}}}-\sqrt {3}\sqrt [3]{-{\frac {a}{{b}^{3}{{\it \_g}}^{3}}}}b+2\,\sqrt {3}a \right ) }{d{\it \_g}}-{\it \_C2}=0 \right \} \]