The solution of the equation $\mathrm{d}y/\mathrm{d}x=\cos (x-y),y\left(\frac{3\pi }{2}\right)=\pi$ is.

Putting $u=x-y,\text{ we get }\mathrm{d}u/\mathrm{d}x=1-\mathrm{d}y/\mathrm{d}x$

The given equation can be written as $1-\mathrm{d}u/\mathrm{d}x=\cos u$ 

$\begin{array}{l}\Rightarrow (1-\cos u)=\mathrm{d}u/\mathrm{d}x\\ \Rightarrow \int \frac{\mathrm{d}u}{1-\cos u}=\mathrm{d}x\Rightarrow \frac{1}{2}\int {\mathrm{cosec}}^2(u/2)\mathrm{d}u=\mathrm{d}x\end{array}$

$\Rightarrow x+\cot (u/2)=\text{ const. }\text{ or }x+\cot \frac{x-y}{2}=C$

Putting $y\left(\frac{3\pi }{2}\right)=\pi ,\frac{3\pi }{2}+1=C$