2.422   ODE No. 422

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

\[ x y'(x)^2-2 y(x) y'(x)+4 x=0 \] Mathematica : cpu = 0.054299 (sec), leaf count = 81

\[\left \{\left \{y(x)\to -\frac {2 \left (x \tanh ^2\left (\frac {1}{2} (c_1-\log (x))\right )+x\right )}{\tanh ^2\left (\frac {1}{2} (c_1-\log (x))\right )-1}\right \},\left \{y(x)\to -\frac {2 \left (x \tanh ^2\left (\frac {1}{2} (c_1+\log (x))\right )+x\right )}{\tanh ^2\left (\frac {1}{2} (c_1+\log (x))\right )-1}\right \}\right \}\] Maple : cpu = 0.049 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) =-2\,x,y \left ( x \right ) =2\,x,y \left ( x \right ) ={\frac {4\,{{\it \_C1}}^{2}+{x}^{2}}{2\,{\it \_C1}}} \right \} \]