3.12   ODE No. 12

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

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

Mathematica: cpu = 0.063008 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to \frac {e^{2 x}-e^{2 c_1}}{e^{2 c_1}+e^{2 x}}\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 8 \[ \left \{ y \left ( x \right ) =\tanh \left ( x+{\it \_C1} \right ) \right \} \]

Sage: cpu = 0.06 (sec), leaf count = 0 \[ \left [\frac {1}{2} \, \log \left (y\left (x\right ) + 1\right ) - \frac {1}{2} \, \log \left (y\left (x\right ) - 1\right ) = c + x, \text {\texttt {separable}}\right ] \]