Thank you for reporting, we will resolve it shortly
Q.
The difference between degree and order of a
differential equation that represents the family of
curves given by $y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right), a>0$ is
$y ^{2}= a \left( x +\frac{\sqrt{ a }}{2}\right)= ax +\frac{ a ^{3 / 2}}{2} \,\,\, \ldots (1)$
$\Rightarrow 2 y y^{\prime}=a$
put in equation (1)
$y^{2}=\left(2 y y^{\prime}\right) x+\frac{\left(2 y y^{\prime}\right)^{3 / 2}}{2}$
$\left(y^{2}-2 x y y^{\prime}\right)=\frac{\left(2 y y^{\prime}\right)^{3 / 2}}{2}$
squaring
$\left(y^{2}-2 x y y^{\prime}\right)^{2}=\frac{y^{3}\left(y^{\prime}\right)^{3}}{2}$
$\therefore $ order $=1$
degree $=3$
Degree $-$ order $=3-1=2$