Match List-I with List-II
| List-I | List-II |
| Differential equation | Order and degree |
| (A) \( \displaystyle\frac{d^4y}{dx^4}+\sin\left(\displaystyle\frac{d^3y}{dx^3}\right)=0 \) | (I) order = 2, degree = 1 |
| (B) \( \left(\displaystyle\frac{d^2y}{dx^2}\right)^2+\displaystyle\frac{dy}{dx}=0 \) | (II) order = 3, degree = 1 |
| (C) \( \displaystyle\frac{d^3y}{dx^3}+y^2+\displaystyle\frac{dy}{dx}=0 \) | (III) order = 2, degree = 2 |
| (D) \( 3y\displaystyle\frac{d^2y}{dx^2}+\left(\displaystyle\frac{dy}{dx}\right)^4=0 \) | (IV) order = 4, degree not defined |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
The order is the highest derivative present; the degree is the power of that derivative, defined only when the equation is a polynomial in the derivatives.
(A) \( \displaystyle\frac{d^4y}{dx^4}+\sin\left(\displaystyle\frac{d^3y}{dx^3}\right)=0 \)
This matches (IV) order = 4, degree not defined. The highest derivative is of fourth order, but a derivative appears inside sin, so the degree is not defined.
(B) \( \left(\displaystyle\frac{d^2y}{dx^2}\right)^2+\displaystyle\frac{dy}{dx}=0 \)
This matches (III) order = 2, degree = 2. \( \frac{d^2y}{dx^2} \) appears squared.
(C) \( \displaystyle\frac{d^3y}{dx^3}+y^2+\displaystyle\frac{dy}{dx}=0 \)
This matches (II) order = 3, degree = 1. \( \frac{d^3y}{dx^3} \) appears to power 1.
(D) \( 3y\displaystyle\frac{d^2y}{dx^2}+\left(\displaystyle\frac{dy}{dx}\right)^4=0 \)
This matches (I) order = 2, degree = 1. \( \frac{d^2y}{dx^2} \) appears to power 1; the power 4 is on the lower derivative.
So the matching is (A) - (IV), (B) - (III), (C) - (II), (D) - (I).