Match List-I with List-II

List-I (Differential equation)	List-II (The sum of degree and order of the differential equation)
(A) $x\frac{d^2y}{dx^2} = \left(1+\left(\frac{dy}{dx}\right)^2\right)^{\frac{1}{3}}$	(I) 2
(B) $x\frac{d^2y}{dx^2} = \left(2-\frac{dy}{dx}\right)^{\frac{1}{7}}$	(II) 9
(C) $3+\frac{dy}{dx} = y+\frac{d^3y}{dx^3}$	(III) 4
(D) $\frac{dy}{dx} = x+3$	(IV) 5

Choose the correct answer from the options given below:

The general solution of the differential equation $x(1 + y^2)dx + y(1 + x^2)dy = 0$ is

Solution of differential equation $\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}$ is:

(where C is an arbitrary constant)

The sum of order and degree of the differential equation $(x^2\frac{d^2y}{dx^2})^{3/4} = 5(\frac{dy}{dx})^2 - 3$ is equal to

If the solution curve of the differentiable equation $\frac{dy}{dx} + 2y = e^{3x}$, passes through the point $\left(0, \frac{6}{5}\right)$, then the value of $y(\log_e 2)$ is:

The general solution of differential equation $\frac{dy}{dx} = e^{x+y}$ is

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: