2.104   ODE No. 104

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

\[ a x y(x)^2+b x+x y'(x)+2 y(x)=0 \] Mathematica : cpu = 0.0175414 (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 = 0.093 (sec), leaf count = 63

\[ \left \{ y \left ( x \right ) =-{\frac {1}{a} \left ( -{\frac {1}{x} \left ( i\sqrt {a}\sqrt {b}x-1 \right ) }+{1{{\rm e}^{-2\,ix\sqrt {a}\sqrt {b}}} \left ( {\it \_C1}-{{\frac {i}{2}}{{\rm e}^{-2\,ix\sqrt {a}\sqrt {b}}}{\frac {1}{\sqrt {a}}}{\frac {1}{\sqrt {b}}}} \right ) ^{-1}} \right ) } \right \} \]