2.176   ODE No. 176

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

\[ \left (x^2-1\right ) x y'(x)+\left (x^2-1\right ) y(x)^2-x^2=0 \] Mathematica : cpu = 0.144153 (sec), leaf count = 73

\[\left \{\left \{y(x)\to -\frac {2 \left (\pi G_{2,2}^{2,0}\left (x^2|\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,1 \\\end {array}\right )+c_1 \left (K\left (x^2\right )-E\left (x^2\right )\right )\right )}{\pi G_{2,2}^{2,0}\left (x^2|\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right )+2 c_1 E\left (x^2\right )}\right \}\right \}\]

Maple : cpu = 0.103 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{\it EllipticCE} \left ( x \right ) +{\it EllipticE} \left ( x \right ) -{\it EllipticK} \left ( x \right ) }{{\it \_C1}\,{\it EllipticCE} \left ( x \right ) -{\it \_C1}\,{\it EllipticCK} \left ( x \right ) +{\it EllipticE} \left ( x \right ) }} \right \} \]