CUET Mathematics 2025 21 May Shift 1 PYQs

Consider the differential equation, $x\frac{dy}{dx} = y(log_e y - log_e x + 1)$, then which of the following are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(C) Its general solution is $log_e\left(\frac{y}{x}\right) = Cx$, where C is constant of integration

(D) Its general solution is $log_e\left(\frac{x}{y}\right) = Cy$, where C is constant of integration

(E) If $y(1) = 1$, then its particular solution is $y = x$

Choose the correct answer from the options given below:

Match List-I with List-II

List-I	List-II
Differential Equation	Degree
(A) $xy\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 - y\frac{dy}{dx} = 0$	(I) 3
(B) $\frac{d^2y}{dx^2} + \log\left(\frac{dy}{dx}\right) = 0$	(II) 1
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + \frac{dy}{dx} + 1 = 0$	(III) not defined
(D) $2x^2\left(\frac{d^2y}{dx^2}\right)^3 - 5\left(\frac{dy}{dx}\right)^3 + y = 0$	(IV) 2

Choose the correct answer from the options given below:

Match List-I with List-II

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^3 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^2 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Choose the correct answer from the options given below: