Field of Extremal - Euler-Lagrange

Question

I need to construct a field of extremals for the functional $J=\int_1^2 t^2 \dot{x}^2 + 2x^2 dt$. With the initial conditions $x(1)=0$ and $x(2)=7$. I know the first step is to use Euler-Lagrange but I'm struggling to compute $\frac{\delta f}{\delta x}-\frac{d}{d t}(\frac{\delta f}{\delta \dot{x}})=0$. How do i solve $4x-\frac{d}{d t}(2t^2\dot{x})=0$?