Particular Integral of $\ln(ax+by)$

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I was wondering what should be particular integral in case of $ln(ax+by)$.

In case it is homogeneous equation : $$P.I = (F(a,b))^{-1}\iiint \ln(v) \ dv\ dv\ \ldots$$ $$ v = ax+by $$

F(a,b) by putting values in differential equation.

Number of $dv$ depending upon order of homogeneous equation.

However, what would be P.I in case of non-homogeneous equation ?