in  this soln part i didnt get after (((log(1-y)=x+logc)))) . in the next line why there is a minus sign before log(1-y)??? because when logc is bring to the left side it should be -ve but why log(1-y)is -ve?:


Now, Integrating both sides, we Get:

$$\begin{gathered} \int \frac{dy}{1-y} = \int dx \\ \Rightarrow \log \left(1-y\right)=x+\log C \\ \Rightarrow -\log C-\log \left(1-y\right)=x \\ \Rightarrow \log C \left(1-y\right)=-x \\ \Rightarrow C(1-y) =e^{-x} \\ \Rightarrow 1-y=\frac{1}{c}{e}^{-x} \\ \Rightarrow y=1-\frac{1}{c}{e}^{-x} \\ \Rightarrow y=A{e}^{-x}\left(Where A=-\frac{1}{c}\right) \end{gathered}$$ $$\begin{gathered} \int \frac{dy}{1-y} = \int dx \\ \Rightarrow \log \left(1-y\right)=x+\log C \\ \Rightarrow -\log C-\log \left(1-y\right)=x \\ \Rightarrow \log C \left(1-y\right)=-x \\ \Rightarrow C(1-y) =e^{-x} \\ \Rightarrow 1-y=\frac{1}{c}{e}^{-x} \\ \Rightarrow y=1-\frac{1}{c}{e}^{-x} \\ \Rightarrow y=A{e}^{-x}\left(Where A=-\frac{1}{c}\right) \end{gathered}$$