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CUET Mathematics 2025 PYQs2 June Shift 1. Free, no login required.

Calculus

past year questions, CUET Mathematics 2025 2 June Shift 1

Differential Equations

past year questions, Calculus, CUET Mathematics 2025 2 June Shift 1

Medium

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The solution of the differential equation ydx+(x−y2)dy=0ydx + (x - y^2)dy = 0 is

Solution

✅ Correct Option: 3

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Related questions:

2023: 23 May Shift 3

Which of the following differential equation represents the family of circles touching the x-axis at the origin ?

2025: 3 June Shift 1

Match List-I with List-II

List-IList-II
Differential EquationSum of order and degree
(A) d2ydx2+dydx+3y=sin⁡x\frac{d^2y}{dx^2} + \frac{dy}{dx} + 3y = \sin x(I) 2
(B) dydx=sin⁡(x+y)\frac{dy}{dx} = \sin(x + y)(II) 3
(C) 1+(dydx)2=d2ydx2\sqrt{1 + (\frac{dy}{dx})^2} = \frac{d^2y}{dx^2}(III) 4
(D) x2(d2ydx2)3+y(dydx)4+y5=0x^2(\frac{d^2y}{dx^2})^3 + y(\frac{dy}{dx})^4 + y^5 = 0(IV) 5

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2026: 29 May Shift 2

In reference to the differential equation : y′′+y=(e)y′y''+y=(e)^{y'}, which of the following statements are correct ?

A. The order of the differential equation is 1.

B. The degree of the differential equation is 1.

C. The order of the differential equation is 2.

D. The degree of the differential equation is not defined.

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2026: 15 May Shift 1

If cc is an arbitrary constant, then

Match the LIST-I with LIST-II

LIST-I (Differential Equation)LIST-II (Solution)
A.dydx=1+x+y+xy\dfrac{dy}{dx} = 1 + x + y + xyI.log⁡e∣y∣=2x+log⁡e(x−1)2+c\log_e \vert y \vert = 2x + \log_e (x-1)^2 + c
B.(x−1)dydx=2xy(x-1)\dfrac{dy}{dx} = 2xyII.y=cxy = cx
C.dydx=1−x+y−xy\dfrac{dy}{dx} = 1 - x + y - xyIII.log⁡e∣1+y∣=x+x22+c\log_e \vert 1+y \vert = x + \dfrac{x^2}{2} + c
D.x dy=y dxx\,dy = y\,dxIV.log⁡e∣1+y∣=x−x22+c\log_e \vert 1+y \vert = x - \dfrac{x^2}{2} + c

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2022: 30 Aug Shift 1

The solution of the differential equation (x+1)dydx=1+y(x+1)\frac{dy}{dx} = 1 + y is

2025: 16 May Shift 1

The degree of the differential equation (2+(dydx)2)32=a2d2ydx2\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2} is:

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