How Can I Solve This 2D Kinetics Problem with Time-Dependent Reactions?

[EzequielJC]

Homework Statement

Hi, I've been trying to solve this exercise for the last four hours and I'm totally stuck. The problems goes like this:

Given the mechanism in the image, located in the vertical plane, the OB cord is cut when t=0. Find the reactions Rx, Ry and N in {Kgf} for the instants when t=0s, t=0.2s and t=0.4s. The initial values are θ(0)=60° and θ'(0)=0. Both rods have mass m=25kg and length L=3m
(i uploaded a image showing the mechanism)

Homework Equations

The first thing I realized was that the three reactions were time/angle dependent, so I inmediately thought of solving this problem with energy considerations, instead of Newton laws. To do this I choose my system to be both rods so the external forces are the gravity and the three reactions. Also, those reactions don't do any work to the system so in terms of equation I got:
(initial kinetic energy) + (initial potential energy) = (final kinetic energy) + (final potential energy)

The Attempt at a Solution

The problem I'm facing here is this, I get a real nasty looking differential equation with no analytic solution. This is preventing me to find θ(t). Also, i not sure if this is really the approach i should be following, is there any easier way I am not taking into account?

 

[EzequielJC]

I decided to use the lagrangian to get the differential equation in the generalized coordinate θ to obtain its differential equation. I've got this
(I₀+I_cr)θ'' + (mgLcosθ)θ' = 0
I_cr is the moment of inertia of the second rod with respect to its instantaneus center of rotation.
Ok so I solved this diff. eq. using wolpram alpha and the solution looks really complicated. I am sure this is not the approach this exercise requires, but I can't seem to figure out any other way, because as i said, the three reactions are not constant. Any idea on this? I would really appreciate any help