Match the LIST-I with LIST-II
| LIST-I Differential equation | LIST-II Sum of order and degree | ||
| A. | \( (y'')^3+xy'+2y=0 \) | I. | 6 |
| B. | \( (y'')^2+(y')^3+4y=0 \) | II. | 3 |
| C. | \( y''+(y')^2+5y=0 \) | III. | 4 |
| D. | \( (y'')^4+3x(y')^2+y=0 \) | IV. | 5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-IV, B-III, C-II, D-I
In each equation the highest derivative is \( y'' \), so the order is 2. The degree is the power of \( y'' \).
(A) \( (y'')^3+xy'+2y=0 \)
This matches IV. 5. Order 2, degree 3, so the sum is 5.
(B) \( (y'')^2+(y')^3+4y=0 \)
This matches III. 4. Order 2, degree 2, so the sum is 4. The power 3 belongs to \( y' \), which is not the highest derivative.
(C) \( y''+(y')^2+5y=0 \)
This matches II. 3. Order 2, degree 1, so the sum is 3.
(D) \( (y'')^4+3x(y')^2+y=0 \)
This matches I. 6. Order 2, degree 4, so the sum is 6.
So the matching is A-IV, B-III, C-II, D-I.