\[ \left (y(x)^2-a^2 x^2\right ) y'(x)^2+\left (1-a^2\right ) x^2+2 x y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.132597 (sec), leaf count = 49
\[\left \{\left \{y(x)\to a c_1-\sqrt {-x^2+c_1{}^2}\right \},\left \{y(x)\to a c_1+\sqrt {-x^2+c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.193 (sec), leaf count = 161
\[\left \{y \left (x \right ) = x \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {-\textit {\_a}^{3}+\textit {\_a} \,a^{2}-\textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-a^{4}+a^{2}}}{\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2}-a^{2}+1\right )}d \textit {\_a} -\ln \left (x \right )\right ), y \left (x \right ) = x \RootOf \left (c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{3}-\textit {\_a} \,a^{2}+\textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-a^{4}+a^{2}}}{\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2}-a^{2}+1\right )}d \textit {\_a} \right )-\ln \left (x \right )\right ), y \left (x \right ) = \sqrt {a^{2}-1}\, x, y \left (x \right ) = -\sqrt {a^{2}-1}\, x\right \}\]