3.530   ODE No. 530

\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}-y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]

Maple: cpu = 0.094 (sec), leaf count = 421 \[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{ \it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{4\,{{\it \_a}}^{2}+2\,{\it \_a}\, \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{ \it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\, {\it \_a}-27 \right ) } \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x- \int ^{y \left ( x \right ) }\!24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{ 2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{ \left ( i\sqrt {3}-1 \right ) \left ( 2\,{\it \_a}- \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{ \it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) \left ( -i \sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+4\,{\it \_a}+ \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{ \it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) }}{d{\it \_a}} -{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-24\,{\frac {\sqrt [3]{- 108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{ \left ( i\sqrt {3}+1 \right ) \left ( 2\,{\it \_a}-\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3 }+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) \left ( i\sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+4\,{\it \_a}+\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a} }^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) }}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \]