3.302   ODE No. 302

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

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

Mathematica: cpu = 0.016002 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to \frac {c_1 x-\sqrt {x} \sqrt {c_1^2 x+4}}{2 x}\right \},\left \{y(x)\to \frac {c_1 x+\sqrt {x} \sqrt {c_1^2 x+4}}{2 x}\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 137 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}\,x}\sqrt {-2\,x {\it \_C1}\, \left ( -2\,{\it \_C1}-x+\sqrt {4\,{\it \_C1}\,x+{x}^{2}} \right ) }},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}\,x}\sqrt {-2 \,x{\it \_C1}\, \left ( -2\,{\it \_C1}-x+\sqrt {4\,{\it \_C1}\,x+{x}^{2 }} \right ) }},y \left ( x \right ) =-{\frac {\sqrt {2}}{2\,{\it \_C1}\,x }\sqrt {x{\it \_C1}\, \left ( 2\,{\it \_C1}+x+\sqrt {4\,{\it \_C1}\,x+{ x}^{2}} \right ) }},y \left ( x \right ) ={\frac {\sqrt {2}}{2\,{\it \_C1 }\,x}\sqrt {x{\it \_C1}\, \left ( 2\,{\it \_C1}+x+\sqrt {4\,{\it \_C1} \,x+{x}^{2}} \right ) }} \right \} \]