\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2}{x}^{2} \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( -{a}^{2}+1 \right ) {x}^{2}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.764 (sec), leaf count = 173 \[ \left \{ y \left ( x \right ) =\sqrt {{a}^{2}-1}x,y \left ( x \right ) ={ \it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac { 1}{{{\it \_a}}^{4}-{{\it \_a}}^{2}{a}^{2}+2\,{{\it \_a}}^{2}-{a}^{2}+1 } \left ( -{{\it \_a}}^{3}+{\it \_a}\,{a}^{2}+\sqrt {{{\it \_a}}^{2}{a} ^{2}-{a}^{4}+{a}^{2}}-{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) -\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_a}}^{4}-{{\it \_a}}^{2 }{a}^{2}+2\,{{\it \_a}}^{2}-{a}^{2}+1} \left ( {{\it \_a}}^{3}-{\it \_a }\,{a}^{2}+\sqrt {{{\it \_a}}^{2}{a}^{2}-{a}^{4}+{a}^{2}}+{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) =- \sqrt {{a}^{2}-1}x \right \} \]