2.251   ODE No. 251

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

\[ \left (x^2 y(x)-1\right ) y'(x)+x y(x)^2-1=0 \] Mathematica : cpu = 0.148873 (sec), leaf count = 60

\[\left \{\left \{y(x)\to \frac {1}{x^2}-\frac {\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \},\left \{y(x)\to \frac {1}{x^2}+\frac {\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \}\right \}\] Maple : cpu = 0.016 (sec), leaf count = 51

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