\[ \left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0 \] ✗ Mathematica : cpu = 300.388 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.465 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x,y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( 2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x \right \} \]