Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$

Question

$\begin{array}{1 1} (A)\;2\tan^{-1}(\large\frac{y}{x}) +\log[x^2+y^2] =\large\frac{ \pi}{2} + \log 2. \\(B)\;2\tan^{-1}(\large\frac{y}{x}) - \log[x^2+y^2] =\large\frac{ \pi}{2} + \log 3. \\ (C)\;2\tan^{-1}(\large\frac{y}{x}) + \log[x^2-y^2] =\large\frac{ \pi}{2} + \log 2. \\ (D)\;2\tan^{-1}(\large\frac{y}{x}) + \log[x+y^2] =\large\frac{ \pi}{2} + \log 2.\end{array} $