\[ \left (a^2-x^2\right ) \left (a^2-y(x)^2\right ) y''(x)+\left (a^2-x^2\right ) y(x) y'(x)^2-x \left (a^2-y(x)^2\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.330287 (sec), leaf count = 65
\[\left \{\left \{y(x)\to \frac {1}{2} e^{c_2} \left (\sqrt {x^2-a^2}+x\right )^{-c_1}+\frac {1}{2} a^2 e^{-c_2} \left (\sqrt {x^2-a^2}+x\right )^{c_1}\right \}\right \}\]
✓ Maple : cpu = 0.227 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C2}} \left ( \left ( \left ( x+\sqrt {-{a}^{2}+{x}^{2}} \right ) ^{{\it \_C1}} \right ) ^{2}{{\it \_C2}}^{2}+{a}^{2} \right ) \left ( \left ( x+\sqrt {-{a}^{2}+{x}^{2}} \right ) ^{{\it \_C1}} \right ) ^{-1}} \right \} \]