CUET Mathematics 2022 6 Aug Shift 2 PYQs

Match List I with List II.

List I	List II
A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$	I. order 3, degree 1
B. $\left(\frac{d^2y}{dx^2}\right)^2 = 0$	II. order 2, degree 2
C. $\frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y = 0$	III. order 2, degree 1
D. $\sin\left(\frac{dy}{dx}\right) + 5y = 0$	IV. order 1, degree is not defined

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Match List-I with List-II

List-I	List-II
Differential Equation	Integrating Factor
(A) $y dx + (x - y^3)dy = 0$	(I) $e^{-x}$
(B) $x\frac{dy}{dx} + y = x^2$	(II) $\frac{1}{x}$
(C) $\frac{dy}{dx} - y = e^x$	(III) $y$
(D) $x dy - y dx = x^3 dx$	(IV) $x$

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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.

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