The solution of the differential equation dy/dx = (x+2)/(3-y), (y ≠ 3), y(0) = 0 represents Option 1: Circle Option 2: Straight line Option 3: Parabola Option 4: Ellipse

Answer: Circle. Solution: Separating variables, (3-y)dy = (x+2)dx. Integrating gives 3y-y^2/2 = x^2/2+2x+c, i.e. x^2+y^2+4x-6y+2c = 0. Since the coefficients of x^2 and y^2 are equal and there is no xy term, this represents a circle.

Calculus

Differential Equations

Easy

common

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$

represents

Circle

Straight line

Parabola

Ellipse

✅ Correct Option: 1

Separating variables, $(3-y)dy = (x+2)dx$ .

Integrating gives $3y-\dfrac{y^2}{2} = \dfrac{x^2}{2}+2x+c$ , i.e. $x^2+y^2+4x-6y+2c = 0$ .

Since the coefficients of $x^2$ and $y^2$ are equal and there is no $xy$ term, this represents a circle.

2023: 22 May Shift 3

The differential equation of the family of curves $y = a \sin(bx + c)$ , a and c are parameters, is :

2025: 26 May Shift 2

The solution of the differential equation $xdy - ydx = 0$ represents

2026: 31 May Shift 2

Match the LIST-I with LIST-II

[ $a$ is an arbitrary constant]

	LIST-I Differential Equation		LIST-II Family of curves
A.	$x\,dy - y\,dx = 0$	I.	$x^2 + y^2 = a^2$
B.	$2y\,dx - x\,dy = 0$	II.	$y = ax$
C.	$x\,dx + y\,dy = 0$	III.	$y^2 = 16x + a$
D.	$y\,dy - 8\,dx = 0$	IV.	$x^2 = ay$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

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

Choose the correct answer from the options given below:

2025: 22 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = (1 + x^2)(1 + y^2)$ is (Here C is an arbitrary constant)

2022: 6 Aug Shift 2

Match List I with List II

List I	List II
A. The number of arbitrary constants in the particular solution of differential equation of order 2	I. 1
B. The number of arbitrary constants in the general solution of differential equation of order 2	II. 0
C. The integrating factor of differential equation $\frac{dy}{dx} + \frac{1}{x}y = 3, x > 0$ , is	III. 2
D. For differential equation, $x^2 \frac{dy}{dx} + x = xy, x > 0, \lim_{x \to 0^+} y(x)$ is equal to	IV. $x$

Choose the correct answer from the options given below:

The solution of the differential equation dydx=x+23−y,(y≠3),y(0)=0\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0dxdy​=3−yx+2​,(y=3),y(0)=0 represents

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$

represents