CUET Mathematics 2025 16 May Shift 1 PYQs

Consider the differential equation $xdy = (y + 2x^2)dx$. Then which of the following are TRUE?

(A) It is a homogeneous differential equation.

(B) Product of the order and degree of the differential equation in one.

(C) Integrating factor is x.

(D) General solution of the differential equation is $y = x^3 + Cx$, where C is an arbitary constant.

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Match List-I with List-II

List-I	List-II
(A) Degree of this differential equation $\frac{d^2y}{dx^2} + 2log_e(\frac{d^2y}{dx^2}) = 0$	(I) 1
(B) Order of this differential equation $p(\frac{dy}{dx})^3 + 3y(\frac{d^2y}{dx^2})^3 = 0$	(II) 4
(C) Degree of $\frac{d^3y}{dx^3} + (\frac{d^2y}{dx})^2 = 0$	(III) not defined
(D) Order of the differential equation $2\frac{d^3y}{dx^3} + (\frac{d^2y}{dx^2})^2 = 0$	(IV) 2

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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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