DSolve[Derivative[1][y][x] == ((-1 + a)*(1 + a)*x)/(-F[x^2/2 - (a^2*x^2)/2 + y[x]^2/2] + a^2*F[x^2/2 - (a^2*x^2)/2 + y[x]^2/2] + y[x]),y[x],x]