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 = 0.0849954 (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 = 0.043 (sec), leaf count = 30

\[\left \{y \left (x \right ) = -2 x, y \left (x \right ) = 2 x, y \left (x \right ) = \frac {x^{2}+4 c_{1}^{2}}{2 c_{1}}\right \}\]