Explanation

(c)
Given differential equation is
$2x\ \frac{dy}{dx} - y = 3$
$\Rightarrow 2x\ \frac{dy}{dx} = 3 + y$
$\Rightarrow \ \int_{}^{}{\frac{dy}{3 + y} = \int_{}^{}\frac{dx}{2x}}$
$\Rightarrow \log{(3 + y) = \frac{1}{2}\log{x + \log c}}$
$\Rightarrow \log{(3 + y) = \log{c \bullet \sqrt{x}}}$
$\Rightarrow 3 + y = c \bullet \sqrt{x}$
$\Rightarrow (3 + y)^{2} = c^{2}x$
Which is an equation of a parabola.