Match List I with List II with regard to degree of the Differential Equation.

Choose the correct answer from the options given below:

A-II, B-III, C-IV, D-I

The correct answer is Option (2) → A-II, B-III, C-IV, D-I

Degree of a differential equation is defined only when the equation is a polynomial in derivatives.

(A) $\frac{d^{3}y}{dx^{3}}+\sin y=0$

Highest order derivative $\frac{d^{3}y}{dx^{3}}$ appears to power $1$.

Degree $=1$.

So (A) → (II).

(B) $\left(\frac{dy}{dx}\right)^{4}+\cos\left(\frac{dy}{dx}\right)-1=0$

Derivative appears inside $\cos$, so not a polynomial in derivatives.

Degree is not defined.

So (B) → (III).

(C) $\left(\frac{d^{2}y}{dx^{2}}\right)^{2}+\left(\frac{dy}{dx}\right)^{4}=0$

Highest order derivative is $\frac{d^{2}y}{dx^{2}}$ and its power is $2$.

Degree $=2$.

So (C) → (IV).

(D) $\left(\frac{d^{2}y}{dx^{2}}\right)^{5}+2\left(\frac{d^{3}y}{dx^{3}}\right)^{4}+7=0$

Highest order derivative is $\frac{d^{3}y}{dx^{3}}$ and its power is $4$.

Degree $=4$.

So (D) → (I).

final answer: (A)–(II), (B)–(III), (C)–(IV), (D)–(I)