2.444   ODE No. 444

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

\[ x^2 y'(x)^2-(y(x)-2 x) y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 0.429728 (sec), leaf count = 75

\[\left \{\left \{y(x)\to -\frac {\cosh (2 c_1)-\sinh (2 c_1)}{x \cosh (2 c_1)+x \sinh (2 c_1)-1}\right \},\left \{y(x)\to -\frac {\cosh (2 c_1)-\sinh (2 c_1)}{x \cosh (2 c_1)+x \sinh (2 c_1)+1}\right \}\right \}\] Maple : cpu = 0.837 (sec), leaf count = 120

\[\left \{y \left (x \right ) = \frac {\sqrt {2}\, c_{1}^{3}-2 c_{1}^{2} x}{4 x^{2}-2 c_{1}^{2}}, y \left (x \right ) = \frac {\left (c_{1} \sqrt {2}+2 x \right ) c_{1}^{2}}{-4 x^{2}+2 c_{1}^{2}}, y \left (x \right ) = 4 x, y \left (x \right ) = -\frac {2 \left (-c_{1} \sqrt {2}+x \right ) c_{1}^{2}}{x^{2}-2 c_{1}^{2}}, y \left (x \right ) = -\frac {2 \left (c_{1} \sqrt {2}+x \right ) c_{1}^{2}}{x^{2}-2 c_{1}^{2}}\right \}\]