Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Integrating factor
A.	$\dfrac{dy}{dx} + 3y = e^{-2x}$	I.	$\dfrac{1}{x}$
B.	$x\dfrac{dy}{dx} + y = 3x^2$	II.	$e^{-x}$
C.	$x\dfrac{dy}{dx} - y = 3x^2$	III.	$x$
D.	$\dfrac{dy}{dx} - y = x$	IV.	$e^{3x}$

Choose the correct answer from the options given below:

The particular solution of the differential equation $\frac{dy}{dx} + \frac{3y}{x} = 0$, $y(1) = 1$ is

The degree of the differential equation $\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}$ is:

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :

For the differential equation $x\frac{dy}{dx} + 3y = x^2\log_e x$, which of the following statements are TRUE?

(A) Product of order and degree is 1

(B) Integrating factor is $x^3$

(C) Integrating factor is $3x$

(D) General solution is $y = \frac{x^3}{36}(6\log_e|x| - 1) + Cx^{-3}$, C is an arbitrary constant.

Choose the correct answer from the options given below:

Solution of the differential equation $y\log_e y dx - x dy = 0$ is (Where c is an arbitrary constant)