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 = 0.0719883 (sec), leaf count = 81

\[\left \{\left \{y(x)\to -\frac {2 \left (x+x \tanh ^2\left (\frac {1}{2} (-\log (x)+c_1)\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} (-\log (x)+c_1)\right )}\right \},\left \{y(x)\to -\frac {2 \left (x+x \tanh ^2\left (\frac {1}{2} (\log (x)+c_1)\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} (\log (x)+c_1)\right )}\right \}\right \}\] Maple : cpu = 0.062 (sec), leaf count = 30

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