\[ \left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0 \] ✓ Mathematica : cpu = 0.146909 (sec), leaf count = 83
\[\left \{\text {Solve}\left [\sqrt {a-1} \tan ^{-1}\left (\frac {y(x)}{x}\right )-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=\log (x)+c_1,y(x)\right ],\text {Solve}\left [\sqrt {a-1} \tan ^{-1}\left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 2.266 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x,y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( 2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x \right \} \]