Solution of differential equation x dy - y dx = 0 represents: Option 1: Family of straight lines passing through origin Option 2: Family of parabolas whose vertex is at origin Option 3: Family of circles whose centre is at origin Option 4: Family of straight lines passing through (1,1)

Answer: Family of straight lines passing through origin. Solution: Separating variables gives dy/y = dx/x, so y = x + c and y = cx. As c varies these are straight lines of every slope, all through the origin.

Calculus

Differential Equations

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Solution of differential equation $x\,dy - y\,dx = 0$ represents:

Family of straight lines passing through origin

Family of parabolas whose vertex is at origin

Family of circles whose centre is at origin

Family of straight lines passing through (1,1)

✅ Correct Option: 1

Separating variables gives $\frac{dy}{y} = \frac{dx}{x}$ , so $\log y = \log x + \log c$ and $y = cx$ . As $c$ varies these are straight lines of every slope, all through the origin.

2026: 21 May Shift 1

Match List-I with List-II

List-I (Differential Equation)	List-II (Degree)
(A) $2(y'')^2 + 3y = 6$	(I) 4
(B) $2y + 5(y')^4 = 7$	(II) 1
(C) $\log x + (y'')^3 = e^x$	(III) 2
(D) $\sqrt{1-2y'} = 5(y'')^{\frac{1}{4}}$	(IV) 3

Choose the correct answer from the options given below:

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Sum of the order and the degree of the differential equation
A.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$	I.	$2$
B.	$4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$	II.	$3$
C.	$x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$	III.	$5$
D.	$\dfrac{dy}{dx} = x^4 e^{-3y}$	IV.	$4$

Choose the correct answer from the options given below:

2025: 15 May Shift 2

The general solution of the differential equation $\frac{xdy}{dx} + 4y = x^3, (x \neq 0)$ is:

2026: 21 May Shift 1

Solution of differential equation $\frac{dy}{dx} = \frac{1+x^2}{1+y^2}$ is

2022: 4 Aug Shift 1

The solution of the differential equation $\frac{dy}{dx} = \frac{\lambda^2}{(x+y)^2}$ ( $\lambda$ is constant) is:

2022: 16 July Shift 2

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

Solution of differential equation x dy−y dx=0x\,dy - y\,dx = 0xdy−ydx=0 represents:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Solution of differential equation $x\,dy - y\,dx = 0$ represents: