Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Differential equation | Order and degree | ||
| (A) | \(\displaystyle\frac{d^3y}{dx^3} + \left(\frac{dy}{dx}\right)^4 = 0\) | (I) | order 2, degree not defined |
| (B) | \(\left(\displaystyle\frac{d^2y}{dx^2}\right)^2 + \displaystyle\frac{dy}{dx} = x\) | (II) | order 3, degree 1 |
| (C) | \(\left(\displaystyle\frac{dy}{dx}\right)^3 = x + y\) | (III) | order 1, degree 3 |
| (D) | \(e^{\frac{d^2y}{dx^2}} = x + y\) | (IV) | order 2, degree 2 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
The order is the order of the highest derivative. The degree is the power of that highest derivative, and it is defined only when the equation is a polynomial in the derivatives.
(A) \(\frac{d^3y}{dx^3} + \left(\frac{dy}{dx}\right)^4 = 0\)
This matches (II) order 3, degree 1. The highest derivative is the third, with power 1; the power 4 belongs to the lower derivative.
(B) \(\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = x\)
This matches (IV) order 2, degree 2. The highest derivative is the second, with power 2.
(C) \(\left(\frac{dy}{dx}\right)^3 = x + y\)
This matches (III) order 1, degree 3. Only the first derivative appears, with power 3.
(D) \(e^{\frac{d^2y}{dx^2}} = x + y\)
This matches (I) order 2, degree not defined. The highest derivative is the second, but it appears in the power of e, and \(e^{\frac{d^2y}{dx^2}}\) is not a polynomial in \(\frac{d^2y}{dx^2}\).