\[ \boxed { 2\, \left ( y \left ( x \right ) \right ) ^{3}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{4}-{a}^{2}x \left ( y \left ( x \right ) \right ) ^{2}-1=0} \]
Mathematica: cpu = 20.022043 (sec), leaf count = 32 \[ \text {DSolve}\left [-a^2 x y(x)^2+2 y(x)^3 y''(x)+y(x)^4-1=0,y(x),x\right ] \]
Maple: cpu = 1.794 (sec), leaf count = 0 \[ \text {could not solve} \]