2.1701   ODE No. 1701

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

\[ -y'(x)^2+y(x) y''(x)-1=0 \] Mathematica : cpu = 0.184532 (sec), leaf count = 80

\[\left \{\left \{y(x)\to -\frac {e^{-c_1} \tanh \left (e^{c_1} (x+c_2)\right )}{\sqrt {-1+\tanh ^2\left (e^{c_1} (x+c_2)\right )}}\right \},\left \{y(x)\to \frac {e^{-c_1} \tanh \left (e^{c_1} (x+c_2)\right )}{\sqrt {-1+\tanh ^2\left (e^{c_1} (x+c_2)\right )}}\right \}\right \}\] Maple : cpu = 1.773 (sec), leaf count = 42

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{2} \left ( \left ( {{\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {x}{{\it \_C1}}}}} \right ) ^{2}+1 \right ) \left ( {{\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{-1} \left ( {{\rm e}^{{\frac {x}{{\it \_C1}}}}} \right ) ^{-1}} \right \} \]