\[ -a^2 x y(x)^2+2 y(x)^3 y''(x)+y(x)^4-1=0 \] ✗ Mathematica : cpu = 44.1747 (sec), leaf count = 0 , could not solve
DSolve[-1 - a^2*x*y[x]^2 + y[x]^4 + 2*y[x]^3*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(2*y(x)^3*diff(diff(y(x),x),x)+y(x)^4-a^2*x*y(x)^2-1=0,y(x))