Match List-I with List-II

Choose the correct answer from the options given below.

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

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

(A) $\frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}+3y=\sin x$ → order $2$, degree $1$ → sum $3$ → (II)

(B) $\frac{dy}{dx}=\sin(x+y)$ → order $1$, degree $1$ → sum $2$ → (I)

(C) $\sqrt{\,1+\left(\frac{dy}{dx}\right)^{2}\,}=\frac{d^{2}y}{dx^{2}}$ Square: $1+\left(\frac{dy}{dx}\right)^{2}=\left(\frac{d^{2}y}{dx^{2}}\right)^{2}$ → order $2$, degree $2$ → sum $4$ → (III)

(D) $x^{2}\left(\frac{d^{2}y}{dx^{2}}\right)^{3}+\left(\frac{dy}{dx}\right)^{4}+y^{3}=0$ Order $2$, degree $3$ → sum $5$ → (IV)

Correct matching: (A)→(II), (B)→(I), (C)→(III), (D)→(IV)