3.509   ODE No. 509

\[ \boxed { 9\, \left ( y \left ( x \right ) \right ) ^{4} \left ( {x}^{2}-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-6\,x \left ( y \left ( x \right ) \right ) ^{5}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -4\,{x}^{2}=0} \]

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

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

Maple: cpu = 1.622 (sec), leaf count = 245 \[ \left \{ y \left ( x \right ) =\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( -{\frac {1}{2}}-{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( -{\frac {1}{2}}+{ \frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( {\frac {1}{2}}-{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( {\frac {1}{2}}+{ \frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) =-\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) ={\frac {1}{2\, {\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}},y \left ( x \right ) =-{\frac {1}{4\,{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{ \it \_C1}}^{2}}}-{\frac {{\frac {i}{4}}\sqrt {3}}{{\it \_C1}}\sqrt [3] { \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}} ,y \left ( x \right ) =-{\frac {1}{4\,{\it \_C1}}\sqrt [3]{ \left ( -16\, {{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}}+{\frac {{ \frac {i}{4}}\sqrt {3}}{{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}} ^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}} \right \} \]