3.421   ODE No. 421

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

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

Mathematica: cpu = 0.032004 (sec), leaf count = 27 \[ \left \{\left \{y(x)\to x \sinh \left (c_1-\log (x)\right )\right \},\left \{y(x)\to x \sinh \left (c_1+\log (x)\right )\right \}\right \} \]

Maple: cpu = 0.437 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) =-ix,y \left ( x \right ) =ix,y \left ( x \right ) =-{\frac {{\it \_C1}}{2} \left ( -{\frac {{x}^{2}}{{{\it \_C1} }^{2}}}+1 \right ) } \right \} \]