How Do I Solve These Coupled Differential Equations Using Lagrange?

[TheTank]

Homework Statement

I used Lagrange to solve a problem and ended up with two differential equations

Homework Equations

$$m_2x''+(k-m_2 {\theta '}^2)x=k(L_o+L_2/2)+m_2 g cos{\theta}$$

and

$$(I_1 +1_2 +m_2 x^2) {\theta}'' +2m_2 \cdot x \cdot x' \theta ' +(m_1 L_1/2 +m_2 x)g sin\theta =0$$

The Attempt at a Solution

I have no idea of how to proceed now.. It doesn't seem that Wolfram Alpha can solve for two differential equations..
Any help at all will be appreciated!

 

[Orodruin]

I suggest you post the full problem rather than simply referring to the stage of the problem you have reached. That way we will know more about where you are and where you want to get to. Without the full problem statement it becomes much more difficult to help you.