\[ -a^2+y(x)^2 y'(x)^2+y(x)^2=0 \] ✓ Mathematica : cpu = 0.0521716 (sec), leaf count = 117
\[\left \{\left \{y(x)\to -\sqrt {a^2-x^2-2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to \sqrt {a^2-x^2-2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to -\sqrt {a^2-x^2+2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to \sqrt {a^2-x^2+2 c_1 x-c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.29 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) =a,y \left ( x \right ) =\sqrt {-{{\it \_C1}}^{2}+2\,{\it \_C1}\,x+{a}^{2}-{x}^{2}},y \left ( x \right ) =-a,y \left ( x \right ) =-\sqrt { \left ( a+x-{\it \_C1} \right ) \left ( {\it \_C1}+a-x \right ) } \right \} \]