2.176   ODE No. 176

\[ \left (x^2-1\right ) x y'(x)+\left (x^2-1\right ) y(x)^2-x^2=0 \] Mathematica : cpu = 0.19405 (sec), leaf count = 82


\[\left \{\left \{y(x)\to \frac {x \left (-2 x G_{2,2}^{2,0}\left (x^2|\begin {array}{c} -\frac {1}{2},\frac {1}{2} \\ -1,0 \\\end {array}\right )+\frac {2 c_1 \left (E\left (x^2\right )-K\left (x^2\right )\right )}{\pi x}\right )}{G_{2,2}^{2,0}\left (x^2|\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right )+\frac {2 c_1 E\left (x^2\right )}{\pi }}\right \}\right \}\] Maple : cpu = 0.095 (sec), leaf count = 30


\[y \relax (x ) = \frac {c_{1} \EllipticCE \relax (x )+\EllipticE \relax (x )-\EllipticK \relax (x )}{c_{1} \EllipticCE \relax (x )-c_{1} \EllipticCK \relax (x )+\EllipticE \relax (x )}\]