With usual notations, in a triangle $A B C$, if $\theta$ is any real number, then $a \cos (B-\theta)+b \cos (A+\theta)$ is

If $A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$, then $A^T A^{-1}=$

The sum of the degree and order of the differential equation $\sqrt{\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}}=\sqrt[5]{\frac{\mathrm{d} y}{\mathrm{~d} x}-5}$ is

The differential equation whose solution represents the family $x^2 y=4 \mathrm{e}^x+\mathrm{c}$, where c is an arbitrary constant, is