\[ \cos ^4(x) \left (y'(x)^2+y(x)^2\right )-a^2=0 \] ✗ Mathematica : cpu = 56.6131 (sec), leaf count = 0 , could not solve
DSolve[-a^2 + Cos[x]^4*(y[x]^2 + Derivative[1][y][x]^2) == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve((diff(y(x),x)^2+y(x)^2)*cos(x)^4-a^2 = 0,y(x))