2.542   ODE No. 542

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

\[ 16 y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.029263 (sec), leaf count = 20

\[\left \{\left \{y(x)\to \sqrt {c_1 x+2 c_1{}^3}\right \}\right \}\] Maple : cpu = 0.508 (sec), leaf count = 107

\[ \left \{ y \left ( x \right ) =\sqrt {16\,{{\it \_C1}}^{3}+2\,{\it \_C1}\,x},y \left ( x \right ) =-{\frac {i}{3}}\sqrt [4]{2}\sqrt [4]{3}\sqrt [4]{-{x}^{3}},y \left ( x \right ) ={\frac {i}{3}}\sqrt [4]{2}\sqrt [4]{3}\sqrt [4]{-{x}^{3}},y \left ( x \right ) =-\sqrt {16\,{{\it \_C1}}^{3}+2\,{\it \_C1}\,x},y \left ( x \right ) =-{\frac {\sqrt [4]{2}\sqrt [4]{3}}{3}\sqrt [4]{-{x}^{3}}},y \left ( x \right ) ={\frac {\sqrt [4]{2}\sqrt [4]{3}}{3}\sqrt [4]{-{x}^{3}}} \right \} \]