\[ \left (a^2-1\right ) x^2 y'(x)^2+a^2 x^2+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.875403 (sec), leaf count = 369
\[\left \{\text {Solve}\left [\frac {a \left (2 \log \left (x-a^2 x\right )-\log \left (\frac {\left (a^2-1\right ) \left (y(x)+i x \left (a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}+a^2-1\right )\right )}{a^3 (x+i y(x))}\right )+\log \left (\frac {i \left (a^2-1\right ) \left (x \left (a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}+a^2-1\right )+i y(x)\right )}{a^3 (x-i y(x))}\right )+\log \left (\frac {y(x)^2}{x^2}+1\right )\right )-2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )}{2 \left (a^2-1\right )}=c_1,y(x)\right ],\text {Solve}\left [\frac {2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \left (2 \log \left (x-a^2 x\right )-\log \left (\frac {\left (a^2-1\right ) \left (y(x)-i x \left (a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}+a^2-1\right )\right )}{a^3 (x-i y(x))}\right )+\log \left (-\frac {i \left (a^2-1\right ) \left (x \left (a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}+a^2-1\right )-i y(x)\right )}{a^3 (x+i y(x))}\right )+\log \left (\frac {y(x)^2}{x^2}+1\right )\right )}{2 \left (a^2-1\right )}=c_1,y(x)\right ]\right \}\]
✓ Maple : cpu = 4.434 (sec), leaf count = 229
\[ \left \{ {\frac {1}{2\,a} \left ( -2\,a{\it \_C1}+2\,a\ln \left ( x \right ) +\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) a-2\,\sqrt {-{a}^{2}}\arctan \left ( {\frac {{a}^{2}y \left ( x \right ) }{\sqrt {-{a}^{2}}x}{\frac {1}{\sqrt {{\frac { \left ( y \left ( x \right ) \right ) ^{2}+ \left ( -{a}^{2}+1 \right ) {x}^{2}}{{x}^{2}}}}}}} \right ) +2\,\ln \left ( {\frac {1}{x} \left ( \sqrt {{\frac {-{a}^{2}{x}^{2}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}x+y \left ( x \right ) \right ) } \right ) \right ) }=0,{\frac {1}{2\,a} \left ( -2\,a{\it \_C1}+2\,a\ln \left ( x \right ) +\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) a+2\,\sqrt {-{a}^{2}}\arctan \left ( {\frac {{a}^{2}y \left ( x \right ) }{\sqrt {-{a}^{2}}x}{\frac {1}{\sqrt {{\frac { \left ( y \left ( x \right ) \right ) ^{2}+ \left ( -{a}^{2}+1 \right ) {x}^{2}}{{x}^{2}}}}}}} \right ) -2\,\ln \left ( {\frac {1}{x} \left ( \sqrt {{\frac {-{a}^{2}{x}^{2}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}x+y \left ( x \right ) \right ) } \right ) \right ) }=0 \right \} \]