Match List-I with List-II | List-I | List-II | |---|---| | (Differential equation) | (Order and Degree) | | (A) $\frac{d^3y}{dx^3} + y^2 + e^{dy/dx} = 0$ | (I) order = 3, degree = 1 | | (B) $\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} + 1 = 0$ | (II) order = 3, degree not defined | | (C) $2x^2\frac{d^2y}{dx^2} - 3\left(\frac{dy}{dx}\right)^2 + y = 0$ | (III) order = 2, degree = 3 | | (D) $\frac{d^3y}{dx^3} + 2\left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$ | (IV) order = 2, degree = 1 | Choose the correct answer from the options given below:

The general solution of the differential equation $\frac{dy}{dx} = e^{x-y} + x^2e^{-y}$ is equal to:

The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

If curve represented by differential equation $x \frac{dy}{dx} + y = e^x$ passes through (1, 1), then $y(-1)$ is :

Solution of the differential equation

$\frac{dy}{dx} = \sqrt{1 + x^2 + y^2 + x^2y^2}$ is : (Here $C$ is an arbitrary constant)

Consider the differential equation $xdy = (x + y) dx$. Which of the following are true?

(A) It is a homogenous differential equation

(B) It is a differential equation of order 2

(C) The general solution of the differential equation contains 2 arbitrary constants

(D) Integrating factor of differential equation is $\frac{1}{x}$

(E) Degree of the differential equation is not defined

Choose the correct answer from the options given below:

General solution of the differential equation $\dfrac{3ydx - 2xdy}{y} = 0$ is :

[where $c$ is an arbitrary constant]