8.86   ODE No. 1676

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

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

Mathematica: cpu = 54.698946 (sec), leaf count = 133 \[ \left \{\left \{y(x)\to x \left (c_2+\int _1^x \frac {i \sqrt {a} \sqrt {b} Y_1\left (-i \sqrt {a} \sqrt {b} K[2]\right )-i \sqrt {a} \sqrt {b} c_1 J_1\left (i \sqrt {a} \sqrt {b} K[2]\right )}{a K[2] \left (c_1 J_0\left (i \sqrt {a} \sqrt {b} K[2]\right )+Y_0\left (-i \sqrt {a} \sqrt {b} K[2]\right )\right )} \, dK[2]\right )\right \}\right \} \]

Maple: cpu = 0.920 (sec), leaf count = 110 \[ \left \{ y \left ( x \right ) = \left ( \int \!-{\frac {{\it \_C1}}{ax}{ {\sl Y}_{1}\left (\sqrt {-ab}x\right )}\sqrt {-ab} \left ( {\it \_C1}\,{ {\sl Y}_{0}\left (\sqrt {-ab}x\right )}+{{\sl J}_{0}\left (\sqrt {-ab}x \right )} \right ) ^{-1}}-{\frac {1}{ax}{{\sl J}_{1}\left (\sqrt {-ab}x \right )}\sqrt {-ab} \left ( {\it \_C1}\,{{\sl Y}_{0}\left (\sqrt {-ab}x \right )}+{{\sl J}_{0}\left (\sqrt {-ab}x\right )} \right ) ^{-1}} \,{\rm d}x+{\it \_C2} \right ) x \right \} \]