Explanation

(d)
Given differential equation is
$x\ dy = y\ dx$
$\Rightarrow$ $\frac{dy}{y} = \frac{dx}{x} \Rightarrow \int_{}^{}\frac{dy}{y} = \int_{}^{}\frac{dx}{x}$
$\Rightarrow$ $\log_{e}y = \log_{e}x + \log_{e}c$
$\Rightarrow$ $y = cx$
Which is a straight line.