2.284   ODE No. 284

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

\[ \left (x^2+4 y(x)^2\right ) y'(x)-x y(x)=0 \] Mathematica : cpu = 0.103978 (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 = 0.097 (sec), leaf count = 21

\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {1}{2}{\it lambertW} \left ( {\frac { \left ( {{\rm e}^{{\it \_C1}}} \right ) ^{2}{x}^{2}}{4}} \right ) }-{\it \_C1}}} \right \} \]