2.1753   ODE No. 1753

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

\[ 12 y(x) y''(x)-15 y'(x)^2+8 y(x)^3=0 \] Mathematica : cpu = 0.560417 (sec), leaf count = 43

\[\left \{\left \{y(x)\to \frac {2304 c_1{}^2}{\left (3 c_1{}^2 x^2+6 c_2 c_1{}^2 x+128+3 c_2{}^2 c_1{}^2\right ){}^2}\right \}\right \}\] Maple : cpu = 1.294 (sec), leaf count = 147

\[\left \{-c_{2}-x -\frac {12 \left (-c_{1}+8 \sqrt {y \left (x \right )}\right ) \sqrt {-c_{1} \sqrt {y \left (x \right )}+8 y \left (x \right )}\, y \left (x \right )}{\sqrt {3 c_{1} y \left (x \right )^{\frac {5}{2}}-24 y \left (x \right )^{3}}\, \sqrt {\left (-c_{1}+8 \sqrt {y \left (x \right )}\right ) \sqrt {y \left (x \right )}}\, c_{1}} = 0, -c_{2}-x +\frac {12 \left (-c_{1}+8 \sqrt {y \left (x \right )}\right ) \sqrt {-c_{1} \sqrt {y \left (x \right )}+8 y \left (x \right )}\, y \left (x \right )}{\sqrt {3 c_{1} y \left (x \right )^{\frac {5}{2}}-24 y \left (x \right )^{3}}\, \sqrt {\left (-c_{1}+8 \sqrt {y \left (x \right )}\right ) \sqrt {y \left (x \right )}}\, c_{1}} = 0\right \}\]