Match List I with List II
| List I | List II : Order and degree respectively | ||
| A. | \(\displaystyle\frac{dy}{dx}-\left(x^2+3\right)=0\) | I. | 2 and 1 |
| B. | \(2x^2\displaystyle\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\) | II. | 2 and 3 |
| C. | \(y'''+y^2+e^{y'}=0\) | III. | 1 and 1 |
| D. | \(\left(\displaystyle\frac{ds}{dt}\right)^4+3s\left(\frac{d^2s}{dt^2}\right)^3=0\) | IV. | 3 and not defined |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-III, B-I, C-IV, D-II
The order is the order of the highest derivative present. The degree is the power of that derivative when the equation is a polynomial in the derivatives; otherwise the degree is not defined.
(A) \(\frac{dy}{dx}-\left(x^2+3\right)=0\)
This matches (III) 1 and 1. The highest derivative is \(\frac{dy}{dx}\), with power 1.
(B) \(2x^2\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\)
This matches (I) 2 and 1. The highest derivative is \(\frac{d^2y}{dx^2}\), with power 1.
(C) \(y'''+y^2+e^{y'}=0\)
This matches (IV) 3 and not defined. The highest derivative is y’’’, but the term \(e^{y'}\) is not a polynomial in y’, so the degree is not defined.
(D) \(\left(\frac{ds}{dt}\right)^4+3s\left(\frac{d^2s}{dt^2}\right)^3=0\)
This matches (II) 2 and 3. The highest derivative is \(\frac{d^2s}{dt^2}\), with power 3 (the power 4 on \(\frac{ds}{dt}\) does not decide the degree).
So the matching is A-III, B-I, C-IV, D-II.