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 = 0.0121921 (sec), leaf count = 57

\[\left \{\left \{y(x)\to \frac {1-\sqrt {c_1 x^2+2 x^3+1}}{x^2}\right \},\left \{y(x)\to \frac {\sqrt {c_1 x^2+2 x^3+1}+1}{x^2}\right \}\right \}\]

Maple : cpu = 0.02 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( 1-\sqrt {-2\,{x}^{2}{\it \_C1}+2\,{x}^{3}+1} \right ) },y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( 1+\sqrt {-2\,{x}^{2}{\it \_C1}+2\,{x}^{3}+1} \right ) } \right \} \]