Match List-I with List-II
| List-I | List-II |
| Differential equation | Order and degree |
| (A) \( y'''+x^2(y'')^3+y=0 \) | (I) 3, 2 |
| (B) \( y'''+y^2+e^{y'}=0 \) | (II) 3, 3 |
| (C) \( (y''')^2+x^2(y'')^3+xy=0 \) | (III) 3, 1 |
| (D) \( (y''')^3+x(y'')^2+y=0 \) | (IV) 3, Not defined |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
In each equation the highest derivative is \( y''' \), so the order is 3. The degree is the power of \( y''' \), provided no derivative sits inside a function such as \( e^{u} \).
(A) \( y'''+x^2(y'')^3+y=0 \)
This matches (III) 3, 1. \( y''' \) appears to the power 1.
(B) \( y'''+y^2+e^{y'}=0 \)
This matches (IV) 3, Not defined. \( y' \) appears in an exponent, so the equation is not a polynomial in the derivatives.
(C) \( (y''')^2+x^2(y'')^3+xy=0 \)
This matches (I) 3, 2. \( y''' \) appears squared.
(D) \( (y''')^3+x(y'')^2+y=0 \)
This matches (II) 3, 3. \( y''' \) appears cubed.
So the matching is (A) - (III), (B) - (IV), (C) - (I), (D) - (II).