The difference between degree and order of a differential equation...

${y}^{2} = a\left(x + \dfrac{\sqrt{a}}{2}\right) = ax + \dfrac{{a}^{3 / 2}}{2}$ $. . . \left(1\right)$

$⇒ 2y{y}^{'} = a$

Put in equation \left(1\right)$we get, </p><p>${y}^{2} = \left(2y{y}^{'}\right)x + \dfrac{{\left(2y{y}^{'}\right)}^{3 / 2}}{2}$</p><p>\left({y}^{2} - 2xy{y}^{'}\right) = \dfrac{{\left(2y{y}^{'}\right)}^{3 / 2}}{2}$

Squaring both the sides we get,

${\left({y}^{2} - 2xy{y}^{'}\right)}^{2} = 2{y}^{3}{\left({y}^{'}\right)}^{3}$

$∴$ Order $= 1$

Degree $= 3$

Degree $-$ order $= 3 - 1 = 2$