3.284   ODE No. 284

\[ \boxed { \left ( 4\, \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -xy \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.033004 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to -\frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}}\right \},\left \{y(x)\to \frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}}\right \}\right \} \]

Maple: cpu = 0.094 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {1}{2}{\it lambertW} \left ( {\frac { \left ( {{\rm e}^{{\it \_C1}}} \right ) ^{2}{x}^{2}}{4} } \right ) }-{\it \_C1}}} \right \} \]