Explanation

(c)
$\because y = u^{n}$
$\therefore\ \frac{dy}{dx} = nu^{n - 1}\frac{du}{dx}$
On substituting the values of $y$ and $\frac{dy}{dx}$ in the given equation, then
$2x^{4} \bullet u^{n} \bullet nu^{n - 1}\frac{du}{dx} + u^{4n} = 4x^{6}\$
$\Rightarrow \frac{du}{dx} = \frac{4x^{6} - u^{4n}}{2nx^{4}u^{2n - 1}}$
Since, it is homogeneous. Then, the degree of $4x^{6} - u^{4n}$ and $2nx^{4}u^{2n - 1}$ must be same.
$\therefore 4n = 6$ and $4 + 2n - 1 = 6$
Then, we get $n = \frac{3}{2}$