ODE No. 1730

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

\[ 2 y(x) y''(x)-y'(x)^2-8 y(x)^3=0 \] Mathematica : cpu = 0.482824 (sec), leaf count = 127

\[\left \{\left \{y(x)\to -\frac {1}{2} i \sqrt {c_1} \text {ns}\left (\left .\frac {1}{2} \left (-(-1)^{3/4} \sqrt {2} \sqrt [4]{c_1} x-(-1)^{3/4} \sqrt {2} \sqrt [4]{c_1} c_2\right )\right |-1\right ){}^2\right \},\left \{y(x)\to -\frac {1}{2} i \sqrt {c_1} \text {ns}\left (\left .\frac {1}{2} \left ((-1)^{3/4} \sqrt {2} \sqrt [4]{c_1} x+(-1)^{3/4} \sqrt {2} \sqrt [4]{c_1} c_2\right )\right |-1\right ){}^2\right \}\right \}\] Maple : cpu = 0.109 (sec), leaf count = 53

\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_C1}\,{\it \_a}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_C1}\,{\it \_a}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]