4.28 Variational calculus

condition: Find the extremal of the functional and study it using 2nd order conditions. \[ \begin{array}{l} \int_{0}^{\frac{\pi}{2}}\left(\dot{x}^{2}-x^{2}+4 x \operatorname{sh} t\right) d t \rightarrow \mathrm{extr} \\ x(0)=x\left(\frac{\pi}{2}\right)=0 \end{array} \]