3.422   ODE No. 422

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

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

Mathematica: cpu = 0.046506 (sec), leaf count = 49 \[ \left \{\left \{y(x)\to 2 \left (2 x \sinh ^2\left (\frac {1}{2} \left (c_1-\log (x)\right )\right )+x\right )\right \},\left \{y(x)\to 2 \left (2 x \sinh ^2\left (\frac {1}{2} \left (c_1+\log (x)\right )\right )+x\right )\right \}\right \} \]

Maple: cpu = 0.515 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) =-2\,x,y \left ( x \right ) =2\,x,y \left ( x \right ) =-{\frac {{\it \_C1}}{2} \left ( -{\frac {{x}^{2}}{{{\it \_C1} }^{2}}}-4 \right ) } \right \} \]