If m is the order and n is degree of differential equations, then
Match List-I with List-II
| List-I | List-II | ||
| (Differential Equation) | (2m + n) | ||
| (A) | \( \left(\displaystyle\frac{d^{2}y}{dx^{2}}+\displaystyle\frac{dy}{dx}\right)^{2}=3y+x \) | (I) | 5 |
| (B) | \( \displaystyle\frac{d}{dx}\left(\displaystyle\frac{d^{2}y}{dx^{2}}\right)+\displaystyle\frac{dy}{dx}+x=4 \) | (II) | 6 |
| (C) | \( \left(\displaystyle\frac{dy}{dx}\right)^{4}+\left(\displaystyle\frac{d^{3}y}{dx^{3}}\right)^{2}=3x+y \) | (III) | 7 |
| (D) | \( \displaystyle\frac{d^{2}y}{dx^{2}}+\displaystyle\frac{dy}{dx}+y+x=7 \) | (IV) | 8 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
The order is that of the highest derivative; the degree is the power of that derivative once the equation is a polynomial in the derivatives.
(A) m = 2, n = 2 → \( 2m+n=6 \), which is (II)
(B) The first term is \( \frac{d^{3}y}{dx^{3}} \), so m = 3, n = 1 → \( 2m+n=7 \), which is (III)
(C) m = 3, n = 2 → \( 2m+n=8 \), which is (IV)
(D) m = 2, n = 1 → \( 2m+n=5 \), which is (I)
So the matching is (A) - (II), (B) - (III), (C) - (IV), (D) - (I).