Find the Particular Solution of the Differential Equation $x^{2} d y=y d x$

Multiple Choice

Find the particular solution of the differential equation $x^{2} d y=y d x$ if $y=1$ when $x=1$ .

A) $\frac{1}{y}=-\frac{1}{x}+2$ or $y=\frac{x}{2 x-1}$
B) $\ln y=-\frac{1}{x}+1$ or $y=e^{\frac{-1}{x}+1}$
C) $\ln y=\ln x^{2}$ or $y=x^{2}$
D) $\ln y=-\frac{1}{x}+2$ or $y=e^{\frac{-1}{x}+2}$