\[ \left (a^2-1\right ) x^2 y'(x)^2+a^2 x^2+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 1.062 (sec), leaf count = 327
\[\left \{\text {Solve}\left [\frac {2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \tanh ^{-1}\left (\frac {-a^2-\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )-a \tanh ^{-1}\left (\frac {-a^2+\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \log \left (\frac {y(x)^2}{x^2}+1\right )}{2 a^2-2}=\frac {a \log \left (x-a^2 x\right )}{1-a^2}+c_1,y(x)\right ],\text {Solve}\left [\frac {-2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )-a \tanh ^{-1}\left (\frac {-a^2-\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \tanh ^{-1}\left (\frac {-a^2+\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \log \left (\frac {y(x)^2}{x^2}+1\right )}{2 a^2-2}=\frac {a \log \left (x-a^2 x\right )}{1-a^2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 2.323 (sec), leaf count = 229
\[\left \{\frac {-2 c_{1} a +2 a \ln \left (x \right )+a \ln \left (\frac {x^{2}+y \left (x \right )^{2}}{x^{2}}\right )-2 \sqrt {-a^{2}}\, \arctan \left (\frac {a^{2} y \left (x \right )}{\sqrt {-a^{2}}\, \sqrt {\frac {\left (-a^{2}+1\right ) x^{2}+y \left (x \right )^{2}}{x^{2}}}\, x}\right )+2 \ln \left (\frac {\sqrt {\frac {-a^{2} x^{2}+x^{2}+y \left (x \right )^{2}}{x^{2}}}\, x +y \left (x \right )}{x}\right )}{2 a} = 0, \frac {-2 c_{1} a +2 a \ln \left (x \right )+a \ln \left (\frac {x^{2}+y \left (x \right )^{2}}{x^{2}}\right )+2 \sqrt {-a^{2}}\, \arctan \left (\frac {a^{2} y \left (x \right )}{\sqrt {-a^{2}}\, \sqrt {\frac {\left (-a^{2}+1\right ) x^{2}+y \left (x \right )^{2}}{x^{2}}}\, x}\right )-2 \ln \left (\frac {\sqrt {\frac {-a^{2} x^{2}+x^{2}+y \left (x \right )^{2}}{x^{2}}}\, x +y \left (x \right )}{x}\right )}{2 a} = 0\right \}\]