8.78   ODE No. 1668

\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 1-y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.082010 (sec), leaf count = 60 \[ \left \{\left \{y(x)\to \sqrt {2} \sqrt {c_1+2} \tanh \left (\frac {1}{2} \left (\sqrt {2} \sqrt {c_1+2} \log (x)-2 \sqrt {2} \sqrt {c_1+2} c_2\right )\right )+2\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 24 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( 2\,{\it \_C1}+\tanh \left ( {\frac {\ln \left ( x \right ) -{\it \_C2}}{2\,{\it \_C1}}} \right ) \right ) } \right \} \]