10. (2004 High School League Preliminary Contest, Liaoning Province) Given real numbers $x, y$ satisfy $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$, find the maximum value of the function $U=x+y$.

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10. Let $\left\{\begin{array}{l}x=3 \cos \alpha \\ y=2 \sin \alpha\end{array}\right.$, then $u=3 \cos \alpha+2 \sin \alpha=\sqrt{13} \sin (\alpha+\varphi)$, where $\varphi=\arctan \frac{3}{2}$, so $u=x+y \leqslant \sqrt{13}$