\[ \left (y(x)^2-a^2\right ) y'(x)^2+y(x)^2=0 \] ✓ Mathematica : cpu = 0.0981847 (sec), leaf count = 97
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \tanh ^{-1}\left (\frac {\sqrt {a^2-\text {$\#$1}^2}}{a}\right )\& \right ][-x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \tanh ^{-1}\left (\frac {\sqrt {a^2-\text {$\#$1}^2}}{a}\right )\& \right ][x+c_1]\right \}\right \}\] ✓ Maple : cpu = 0.56 (sec), leaf count = 122
\[\left \{-\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )}{\sqrt {a^{2}}}-c_{1}+x +\sqrt {a^{2}-y \left (x \right )^{2}} = 0, \frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )}{\sqrt {a^{2}}}-c_{1}+x -\sqrt {a^{2}-y \left (x \right )^{2}} = 0\right \}\]