\[ \boxed { \left ( {a}^{2}-{x}^{2} \right ) \left ( {a}^{2}- \left ( y \left ( x \right ) \right ) ^{2} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {a}^{2}-{x}^{2} \right ) y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-x \left ( {a}^{2}- \left ( y \left ( x \right ) \right ) ^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.340043 (sec), leaf count = 66 \[ \left \{\left \{y(x)\to \frac {1}{2} e^{-c_2} \left (\sqrt {x^2-a^2}+x\right )^{-c_1} \left (a^2 \left (\sqrt {x^2-a^2}+x\right )^{2 c_1}+e^{2 c_2}\right )\right \}\right \} \]
Maple: cpu = 1.732 (sec), leaf count = 51 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C2}} \left ( \left ( \left ( x+\sqrt {-{a}^{2}+{x}^{2}} \right ) ^{{\it \_C1}} \right ) ^{2}{ {\it \_C2}}^{2}+{a}^{2} \right ) \left ( \left ( x+\sqrt {-{a}^{2}+{x}^ {2}} \right ) ^{{\it \_C1}} \right ) ^{-1}} \right \} \]