Understand Newtons second law. Equation 833 is separable with fx 6x2 4x and gy 1 Equation 834 is separable with fx 1 and gy secy tany and the right-hand side of Equation 835 can be factored as x 3y 2 so it is separable as well. The question is which kinds motions are not allowed by Newtons second law because of the fact that it is a second order differential equation of the form x f x x t.
The result looks similar to Newtons second law in linear motion with a few modifications.
M d2x dt2 P F fr m d2x dt2 mg x L mmg Lx L d2x dt2 g x L mg L x L d2x dt2 1mg L x mg. In this equation both F and a are vectors with a direction and a magnitude. The way the question is asked doesnt quite work because it leads to a trivial answer. The rotational form of Newtons second law states the relation between net external torque and the angular acceleration of a body about a fixed axis.