3.104   ODE No. 104

\[ \boxed { x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ax \left ( y \left ( x \right ) \right ) ^{2}+2\,y \left ( x \right ) +bx=0} \]

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

Mathematica: cpu = 0.015502 (sec), leaf count = 43 \[ \left \{\left \{y(x)\to -\sqrt {\frac {b}{a}} \tan \left (a x \sqrt {\frac {b}{a}}-c_1\right )-\frac {1}{a x}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) =-{\frac {1}{a} \left ( -{\frac {1}{x} \left ( i\sqrt {a}\sqrt {b}x-1 \right ) }+{1{{\rm e}^{-2\,ix\sqrt {a} \sqrt {b}}} \left ( {\it \_C1}-{{\frac {i}{2}}{{\rm e}^{-2\,ix\sqrt {a} \sqrt {b}}}{\frac {1}{\sqrt {a}}}{\frac {1}{\sqrt {b}}}} \right ) ^{-1} } \right ) } \right \} \]