Given a system composed by a simple pendulum that is abandoned from rest at $t=0$, $\theta(0)=\frac{\pi}{2}$. Find the extremal of the functional for this system:
$J(\theta)=\int(\frac{m}{2}l^2\theta'^2+mgl\cos(\theta))dt$
My approach to the solution
I started by applying the Euler-Lagrange equation, and got the following result:
$-mgl\sin(\theta)-ml^2\theta''=0$
If I got the correct result and understood the problem , now I need to solve this ODE in order to have the Extremal of the given function, is that right?