Match List-I with List-II
|
List-I |
List-II |
|
(A) The degree of differential equation $\frac{d^3y}{dx^3}= e^{\frac{dy}{dx}}$ |
(I) 2 |
|
(B) The order of differential equation $(\frac{dy}{dx})^2\frac{d^3y}{dx^3}=0$ |
(II) 4 |
|
(C) The sum of order and degree of differential equation $\frac{d}{dx}(\frac{d^2y}{dx^2})+(\frac{dy}{dx})^5= x$ |
(III) not defined |
|
(D) The number of arbitrary constants in the general solution of a differential equation of order 2 |
(IV) 3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
|
List-I |
List-II |
|
(A) The degree of differential equation $\frac{d^3y}{dx^3}= e^{\frac{dy}{dx}}$ |
(III) not defined |
|
(B) The order of differential equation $(\frac{dy}{dx})^2\frac{d^3y}{dx^3}=0$ |
(IV) 3 |
|
(C) The sum of order and degree of differential equation $\frac{d}{dx}(\frac{d^2y}{dx^2})+(\frac{dy}{dx})^5= x$ |
(II) 4 |
|
(D) The number of arbitrary constants in the general solution of a differential equation of order 2 |
(I) 2 |
(A) $\frac{d^{3}y}{dx^{3}} = e^{\frac{dy}{dx}}$ Degree is not defined because the highest derivative occurs inside a non-polynomial function (exponential). → (A) → (III)
(B) $\left(\frac{dy}{dx}\right)^{2}\frac{d^{3}y}{dx^{3}}=0$ Highest order derivative = 3 ⇒ order = 3 → (B) → (IV)
(C) $\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)+\left(\frac{dy}{dx}\right)^{5}=x$ Order = 3, degree = 1 ⇒ sum = 4 → (C) → (II)
(D) Differential equation of order 2 has 2 arbitrary constants → (D) → (I)
Correct matching:
(A)–(III), (B)–(IV), (C)–(II), (D)–(I)