Explanation

(a)
The given differential equation can be rewritten as
$y + \frac{d^{2}y}{dx^{2}} = \left\lbrack a + \left( \frac{dy}{dx} \right)^{\frac{3}{2}} \right\rbrack^{2}$
$\Rightarrow$ $y + \frac{d^{2}y}{dx^{2}} = x^{2} + \left( \frac{dy}{dx} \right)^{3} + 2x\left( \frac{dy}{dx} \right)^{\frac{3}{2}}$
$\Rightarrow$ $\left\lbrack y + \frac{d^{2}y}{dx^{2}} - x^{2} - \left( \frac{dy}{dx} \right)^{3} \right\rbrack^{2} = \left\lbrack 2x\left( \frac{dy}{dx} \right)^{\frac{3}{2}} \right\rbrack^{2}$
$\therefore$ Order and degree of the given differential equation is 2 and 2 respectively.