The differential equation \(y \frac{dx}{dy}=y-1,y(0)=1\) has

Unique solution Two solutions infinite number of solution No solution

Unique solution

\(\begin{aligned}\text{Given, }dx&=\left(1-\frac{1}{y}\right)dy\\ \text{So, }x&=y-\log y+c\\ \text{Setting }x=0,y&=1, \text{ we get }c=-1\\ x&=y-\log y-1\end{aligned}\)