DSolve[Derivative[1][y][x] == -((x*(-1 - x^4 + x^6 + 2*x^2*y[x]^2 - 3*x^4*y[x]^2 - y[x]^4 + 3*x^2*y[x]^4 - y[x]^6))/y[x]),y[x],x]