8.14   ODE No. 1604

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

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

Mathematica: cpu = 0.060508 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to \log \left (\frac {1}{2} c_1 \left (\tanh ^2\left (\frac {1}{2} \sqrt {c_1 \left (c_2+x\right ){}^2}\right )-1\right )\right )\right \}\right \} \]

Maple: cpu = 0.281 (sec), leaf count = 23 \[ \left \{ y \left ( x \right ) =\ln \left ( {\frac {1}{2\,{{\it \_C1}}^{2 }} \left ( \left ( \tan \left ( {\frac {{\it \_C2}+x}{2\,{\it \_C1}}} \right ) \right ) ^{2}+1 \right ) } \right ) \right \} \]