Match List-I with List-II
| List-I | List-II | ||
| Differential Equation | Sum of order and degree | ||
| (A) | \(\displaystyle\frac{d^2y}{dx^2}+\frac{dy}{dx} +3y= \sin x\) | (I) | 2 |
| (B) | \(\displaystyle\frac{dy}{dx}=\sin (x + y)\) | (II) | 3 |
| (C) | \(\sqrt{1+\left(\displaystyle\frac{dy}{dx}\right)^2}=\displaystyle\frac{d^2y}{dx^2}\) | (III) | 4 |
| (D) | \(x^2\left(\displaystyle\frac{d^2y}{dx^2}\right)^3+\left(\displaystyle\frac{dy}{dx}\right)^4+ y^3 = 0\) | (IV) | 5 |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
The order is the order of the highest derivative; the degree is the power of that derivative once the equation is a polynomial in the derivatives.
(A) \(\displaystyle\frac{d^2y}{dx^2}+\frac{dy}{dx} +3y= \sin x\)
This matches (II) 3.
\( \text{Order } 2,\ \text{degree } 1,\ \text{sum} = 3 \)
(B) \(\displaystyle\frac{dy}{dx}=\sin (x + y)\)
This matches (I) 2.
\( \text{Order } 1,\ \text{degree } 1,\ \text{sum} = 2 \)
(C) \(\sqrt{1+\left(\frac{dy}{dx}\right)^2}=\frac{d^2y}{dx^2}\)
This matches (III) 4.
The root must be removed first. Squaring both sides:
\( \displaystyle 1 + \left(\frac{dy}{dx}\right)^2 = \left(\frac{d^2y}{dx^2}\right)^2 \)
\( \text{Order } 2,\ \text{degree } 2,\ \text{sum} = 4 \)
(D) \(x^2\left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^4+ y^3 = 0\)
This matches (IV) 5.
\( \text{Order } 2,\ \text{degree } 3,\ \text{sum} = 5 \)
So the matching is (A)-(II), (B)-(I), (C)-(III), (D)-(IV).