3.345   ODE No. 345

\[ \boxed { x \left ( 2\,{x}^{2}y \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) +1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.041005 (sec), leaf count = 35 \[ \text {Solve}\left [\frac {y(x)}{x^2}+2 \left (\frac {1}{2} y(x)^2 \log (y(x))-\frac {y(x)^2}{4}\right )=c_1,y(x)\right ] \]

Maple: cpu = 0.063 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( 2\,{\it \_Z }\,{x}^{2} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-{x}^{2} \left ( { {\rm e}^{{\it \_Z}}} \right ) ^{2}+2\,{x}^{2}{\it \_C1}+2\,{{\rm e}^{{ \it \_Z}}} \right ) }} \right \} \]