Determine the nature of the following differential equations (Order of the equation? Or- dinary or partial? Linear or non-linear? Homogeneous or non-homogeneous? Constant- coefficient or not? How many undetermined constants will appear in a possible solu- tion?) (30 points) swamy 2 = (ii) 2 dy(t) = dt dt (i) sin t dylt + cost = y(t) ) t - |g|t)| = 2 (iii) 2dy(t) y?(t) = 0 ) av (x,y) av (x,y) (v) + (vi) dy(2) + 4cy (iv) 1 dy(t) = 3d12" + 3y(t) = 0 3 = 0 ay e-222 dc