Match List-I with List-II
|
List-I Statement |
List-II Its value |
|
(A) Degree of the differential equation $\frac{d^2y}{dx^2}= e^{dy/dx}$ is |
(I) 2 |
|
(B) Order of the differential equation $\left(\frac{dy}{dx}\right)^2+\frac{d^3y}{dx^3}=0$ is |
(II) not defined |
|
(C) Degree of the differential equation $\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^2- 5x^2 = 0$ |
(III) 3 |
|
(D) If $p$ is the order and $q$ is the degree of the differential equation $\frac{dy}{dx}+3y=e^x$, then $p + q$ is |
(IV) 1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
|
List-I Statement |
List-II Its value |
|
(A) Degree of the differential equation $\frac{d^2y}{dx^2}= e^{dy/dx}$ is |
(II) not defined |
|
(B) Order of the differential equation $\left(\frac{dy}{dx}\right)^2+\frac{d^3y}{dx^3}=0$ is |
(III) 3 |
|
(C) Degree of the differential equation $\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^2- 5x^2 = 0$ |
(IV) 1 |
|
(D) If $p$ is the order and $q$ is the degree of the differential equation $\frac{dy}{dx}+3y=e^x$, then $p + q$ is |
(I) 2 |
Matching the items with explanation:
(A) $\frac{d^2y}{dx^2} = e^{\frac{dy}{dx}}$:
The degree is not defined because the derivative $\frac{dy}{dx}$ is inside the exponential function, which makes the equation non-polynomial. → (II) not defined.
(B) $\left(\frac{dy}{dx}\right)^2 + \frac{d^3y}{dx^3} = 0$:
The order is the highest derivative present, which is $\frac{d^3y}{dx^3}$. The degree is the exponent of this highest-order derivative, which is 1. Thus, the order is $3$. → (III) 3.
(C) $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 - 5x^2 = 0$:
The highest-order derivative is $\frac{d^2y}{dx^2}$, which appears with power 1. Hence, the degree is 2 due to the squared first derivative. → (I) 2.
(D) $\frac{dy}{dx} + 3y = e^x$:
The order is 1, and the degree is also 1 since the first derivative appears linearly. $p + q = 1 + 1 = 2$. → (IV) 1.