Solve for C_1
C_{1}=-\ln(|x-2|)+|y|
x\neq 2
Solve for x
\left\{\begin{matrix}x=2-e^{y-C_{1}}\text{; }x=e^{y-C_{1}}+2\text{, }&y\geq 0\\x=2-e^{-C_{1}-y}\text{; }x=e^{-C_{1}-y}+2\text{, }&y\leq 0\end{matrix}\right.
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