8.80   ODE No. 1670

\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{2}-b=0} \]

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

Mathematica: cpu = 90.651011 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to x \left (\int _1^x \frac {\sqrt {-\frac {b}{a}} \tan \left (c_1-a \sqrt {-\frac {b}{a}} K[2]\right )}{K[2]^2} \, dK[2]+c_2\right )\right \}\right \} \]

Maple: cpu = 0.281 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) = \left ( \int \!{\frac {i}{{x}^{2}}\tan \left ( -i\sqrt {a}\sqrt {b}x+{\it \_C1} \right ) \sqrt {b}{\frac {1}{ \sqrt {a}}}}\,{\rm d}x+{\it \_C2} \right ) x \right \} \]