Which of the following is a homogeneous differential equation ? Option 1: ydx + (x-y^2)dy = 0 Option 2: dy/dx + 2y x = 2x Option 3: x^2dy/dx = xy - 2x^2 + y^2 Option 4: (x^3-y^3)dx + 3xy dy = 0

The answer is 'x^2dy/dx = xy - 2x^2 + y^2'. View full solution:

CUET Mathematics - Which of the following is a homogeneous differential equation ? | PYQs + Solutions

CUET Mathematics 2026 25th May Shift 1

Calculus

Medium

core

$ydx + (x-y^2)dy = 0$

$\dfrac{dy}{dx} + 2y\tan x = 2x$

$x^2\dfrac{dy}{dx} = xy - 2x^2 + y^2$

$(x^3-y^3)dx + 3xy\,dy = 0$

✅ Correct Option: 3

Related questions:

16 May Shift 1

If $\sin y=x \sin (a+y)$ , then $\frac{d y}{d x}$ is :

21st May Shift 2

Match the differential equation (List-I) with its order and degree (List-II)

LIST-I		LIST-II
A. $\dfrac{d^3y}{dx^3} + x^2\left(\dfrac{d^2y}{dx^2}\right) = 0$		I. order =3; degree is not defined
B. $\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$		II. order =3; degree=1
C. $1 - \left(\dfrac{dy}{dx}\right)^2 = \left(a\dfrac{d^2y}{dx^2}\right)^{1/3}$		III. order =2; degree=1
D. $y = x\left(\dfrac{dy}{dx}\right)^3 + \left(\dfrac{d^2y}{dx^2}\right)^4$		IV. order =2; degree=4

Choose the correct answer from the options given below:

30 May Shift 3

Match List - I with List - II. Match the integrating factors :

List - I (Differential Equation)	List - II (Integrating factor)
(A) $\frac{dy}{dx} + 3y = e^{-2x}$	(I) $\frac{1}{x}$
(B) $x\frac{dy}{dx} + y = 3x^2$	(II) $e^{-x}$
(C) $x\frac{dy}{dx} - y = 3x^2$	(III) $x$
(D) $\frac{dy}{dx} - y = x$	(IV) $e^{3x}$

Choose the correct answer from the options given below :