Match List-I with List-II
| List-I (Differential Equation) | List-II (Degree) | ||
| (A) | \( 2(y'')^{2}+3y=6 \) | (I) | 4 |
| (B) | \( 2y+5(y')^{4}=7 \) | (II) | 1 |
| (C) | \( \log x+(y'')^{3}=e^{x} \) | (III) | 2 |
| (D) | \( \sqrt{1-2y'}=5(y'')^{\frac{1}{4}} \) | (IV) | 3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
The degree is the power of the highest-order derivative once the equation is free of radicals and fractional powers.
(A) \( 2(y'')^{2}+3y=6 \)
This matches (III) 2. The highest derivative y″ is squared.
(B) \( 2y+5(y')^{4}=7 \)
This matches (I) 4. The highest derivative y′ has power 4.
(C) \( \log x+(y'')^{3}=e^{x} \)
This matches (IV) 3. The highest derivative y″ is cubed.
(D) \( \sqrt{1-2y'}=5(y'')^{\frac{1}{4}} \)
This matches (II) 1. Raising both sides to the power 4 clears the fractional powers:
\( (1-2y')^{2}=625\,y'' \)
so y″ has power 1.
So the matching is (A) - (III), (B) - (I), (C) - (IV), (D) - (II).