Explanation

(b)
Let $y = f(x)$ be the curve. The equation of tangent at $(x,y)$ to this curve is
$Y - y = f^{'}(x)(X - x)$ ….(i)
Put $X = 0$ in Eq. (i), we get
$Y = y - x\ \ f^{'}(x)$
This ordinate is called the initial ordinate of the tangent. It is given that,
Initial ordinate of the tangent = Subnormal
$\Rightarrow$ $y - x\ f^{'}(x) = y\ \frac{dy}{dx}$
$\Rightarrow$ $\frac{dy}{dx} = \frac{y}{x + y}$ [put $f^{'}(x) = \frac{dy}{dx}$]
Hence, it is a homogenous differential equation.