ODE No. 1714

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

\[ y(x) y''(x)+3 y(x) y'(x)-3 y'(x)^2-y(x)^2=0 \] Mathematica : cpu = 0.0637011 (sec), leaf count = 25

\[\left \{\left \{y(x)\to \frac {c_2 e^x}{\sqrt {1-2 e^{c_1+x}}}\right \}\right \}\] Maple : cpu = 0.082 (sec), leaf count = 68

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