Solve the differential equation (2x³8xy³ - 18x) dx + (12x³y² + 3y³ - 6y³) dy = 0 using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dy = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations JM(u, v) = 0 N(u, v) = 0. Afterwards, apply another substitution r = u-uo, 8 = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class.