ODE No. 1668

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

\[ x y''(x)-(1-y(x)) y'(x)=0 \] Mathematica : cpu = 0.0706216 (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 = 0.182 (sec), leaf count = 24

\[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( 2\,{\it \_C1}+\tanh \left ( {\frac {\ln \left ( x \right ) -{\it \_C2}}{2\,{\it \_C1}}} \right ) \right ) } \right \} \]