\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2}=0} \]
Mathematica: cpu = 0.046506 (sec), leaf count = 107 \[ \left \{\left \{y(x)\to -\frac {a \tan \left (x-c_1\right )}{\sqrt {\tan ^2\left (x-c_1\right )+1}}\right \},\left \{y(x)\to \frac {a \tan \left (x-c_1\right )}{\sqrt {\tan ^2\left (x-c_1\right )+1}}\right \},\left \{y(x)\to -\frac {a \tan \left (c_1+x\right )}{\sqrt {\tan ^2\left (c_1+x\right )+1}}\right \},\left \{y(x)\to \frac {a \tan \left (c_1+x\right )}{\sqrt {\tan ^2\left (c_1+x\right )+1}}\right \}\right \} \]
Maple: cpu = 0.514 (sec), leaf count = 68 \[ \left \{ y \left ( x \right ) =a,y \left ( x \right ) =\tan \left ( -x+{ \it \_C1} \right ) \sqrt {{\frac {{a}^{2}}{ \left ( \tan \left ( -x+{\it \_C1} \right ) \right ) ^{2}+1}}},y \left ( x \right ) =-a,y \left ( x \right ) =-\tan \left ( -x+{\it \_C1} \right ) \sqrt {{\frac {{a}^{2}}{ \left ( \tan \left ( -x+{\it \_C1} \right ) \right ) ^{2}+1}}} \right \} \]