Match List-I with List-II
| List-I Differential Equations | List-II Degree/Order | ||
|---|---|---|---|
| (A) | Degree of the differential equation \(\displaystyle\frac{d^3y}{dx^3}+2\log x.y=0\) | (I) | 3 |
| (B) | Order of the differential equation \(\displaystyle\frac{d^4y}{dx^4}+\left(\frac{dy}{dx}\right)^4+xy=0\) | (II) | 2 |
| (C) | Degree of the differential equation \(\displaystyle\left(\frac{d^4y}{dx^4}\right)^2+\left(\frac{dy}{dx}\right)^3+x^2y=0\) | (III) | 1 |
| (D) | Order of the differential equation \(\displaystyle\frac{d^3y}{dx^3}+y\left(\frac{dy}{dx}\right)^3=0\) | (IV) | 4 |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
The order is the order of the highest derivative present. The degree is the power of that highest derivative, when the equation is a polynomial in the derivatives.
(A) Degree of \(\frac{d^3y}{dx^3}+2\log x.y=0\)
This matches (III) 1. The term \(2\log x.y\) is \(2y\log x\), which contains no derivative, and the highest derivative \(\frac{d^3y}{dx^3}\) appears to the power 1.
(B) Order of \(\frac{d^4y}{dx^4}+\left(\frac{dy}{dx}\right)^4+xy=0\)
This matches (IV) 4. The highest derivative is \(\frac{d^4y}{dx^4}\).
(C) Degree of \(\left(\frac{d^4y}{dx^4}\right)^2+\left(\frac{dy}{dx}\right)^3+x^2y=0\)
This matches (II) 2. The highest derivative \(\frac{d^4y}{dx^4}\) is squared; the cube of \(\frac{dy}{dx}\) does not count, as \(\frac{dy}{dx}\) is not the highest derivative.
(D) Order of \(\frac{d^3y}{dx^3}+y\left(\frac{dy}{dx}\right)^3=0\)
This matches (I) 3. The highest derivative is \(\frac{d^3y}{dx^3}\).
So the matching is (A)-(III), (B)-(IV), (C)-(II), (D)-(I).