\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.282536 (sec), leaf count = 111 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \log \left (a \sqrt {a^2-\text {$\#$1}^2}+a^2\right )+a \log (\text {$\#$1})\& \right ]\left [c_1-x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \log \left (a \sqrt {a^2-\text {$\#$1}^2}+a^2\right )+a \log (\text {$\#$1})\& \right ]\left [c_1+x\right ]\right \}\right \} \]
Maple: cpu = 0.905 (sec), leaf count = 122 \[ \left \{ x-\sqrt {{a}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}+{{ a}^{2}\ln \left ( {\frac {1}{y \left ( x \right ) } \left ( 2\,{a}^{2}+2 \,\sqrt {{a}^{2}}\sqrt {{a}^{2}- \left ( y \left ( x \right ) \right ) ^{ 2}} \right ) } \right ) {\frac {1}{\sqrt {{a}^{2}}}}}-{\it \_C1}=0,x+ \sqrt {{a}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}-{{a}^{2}\ln \left ( {\frac {1}{y \left ( x \right ) } \left ( 2\,{a}^{2}+2\,\sqrt {{a }^{2}}\sqrt {{a}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) {\frac {1}{\sqrt {{a}^{2}}}}}-{\it \_C1}=0 \right \} \]