3.217   ODE No. 217

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

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

Mathematica: cpu = 0.018502 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (W\left (-e^{c_1-2 x^2-1}\right )+1\right )+x^2\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 23 \[ \left \{ y \left ( x \right ) ={x}^{2}+{\frac {{\it lambertW} \left ( -4 \,{\it \_C1}\,{{\rm e}^{-2\,{x}^{2}-1}} \right ) }{2}}+{\frac {1}{2}} \right \} \]