4.27 Variational calculus
Condition: Find admissible extremals of the functional: \[ \int_{-1}^{1}\left(\dot{x}^{2}+4 x^{2}\right) d t \rightarrow \operatorname{extr}, x(-1)=-1, x(1)=1 \]
The calculus of variations is a branch of analysis that studies extreme properties of functionals. Here you can find optimal control problems - including finding the extrema of functionals.