44. Find the smallest positive period and the maximum value of the function

$$
y=3 \sin 2 x+4 \cos 2 x
$$
44. Let's transform the function as follows:

$$
y=3 \sin 2 x+4 \cos 2 x=5 \sin (2 x+\alpha)
$$

where $\alpha=\arcsin \frac{4}{5}$.

From this, it is clear that the maximum value of the function is 5. The smallest positive period is $\pi$.