CUET Mathematics - Particular solution of the differential equation x(1 + y^2)dx - y(1 + x^2)dy = 0, given y = 0 when x = 1, is | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 2

Calculus

Medium

common

$(1 + x^2) = 2(1 + y^2)$

$(1 + y^2) = 2(1 + x^2)$

$(1 + x^2) = 4(1 + y^2)$

$(1 + y^2) = 4(1 + x^2)$

✅ Correct Option: 1

Related questions:

30 May Shift 1

For the differential equation $y\frac{dx}{dx} - (x + 3y^2)dy = 0$ , which of the following statements are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) If $y(0) = 1$ , then its particular solution is $x = 3y^2 - 1$

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21 May Shift 2

The solution of the differential equation $(x + 1)\frac{dy}{dx} + 1 - 2e^{-y} = 0$ , $y(0) = 0$ is

27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^3y}{dx^3} + \left(\frac{dy}{dx}\right)^{1/3} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^3 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

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CUET Mathematics 2025 14 May Shift 2 PYQs