Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Sum of order and degree)
A.	$(y'')^3 + xy' + 2y = 0$	I.	$6$
B.	$(y'')^2 + (y')^3 + 4y = 0$	II.	$3$
C.	$y'' + (y')^2 + 5y = 0$	III.	$4$
D.	$(y'')^4 + 3x(y')^2 + y = 0$	IV.	$5$

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The particular solution of the differential equation $\frac{dy}{dx}=x(2\log x+1)$, given that $y=0$ when $x=2$, is:

(consider $\log x=\log_e x$)

The differential equation representing family of curves $y = e^{-2x}(a \cos x + b \sin x)$, where a and b are arbitrary constant, is :

The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

The general solution of the differential equation $\tan\left(\dfrac{(1+x^2)y'+2xy}{2x}\right)=1+x^2$, is

(Consider $\log_e x=\log x$)

(where C is an arbitrary constant)

For the differential equation $\frac{d}{dx}\left(\frac{d^3y}{dx^3}\right)+\left(\frac{dy}{dx}\right)^3+y+x=7$, which of the following statements are True?

A. Order of differential equation is 4

B. Number of arbitrary constants in the particular solution of differential equation are 4

C. Number of arbitrary constants in the general solution of the differential equation are 4

D. Degree of differential equation is 3

Choose the correct answer from the options given below: