General solution of the differential equation 3ydx - 2xdy/y = 0 is : [where c is an arbitrary constant] Option 1: y = cx^2 Option 2: x^3 = cy^2 Option 3: x = cy^2 Option 4: y^3 = cx^2

The answer is 'x^3 = cy^2'. View full solution:

CUET Mathematics - General solution of the differential equation 3ydx - 2xdy/y = 0 is : [where c is an arbitrary constant] | PYQs + Solutions

CUET Mathematics 2026 25th May Shift 1

Calculus

Easy

common

$y = cx^2$

$x^3 = cy^2$

$x = cy^2$

$y^3 = cx^2$

✅ Correct Option: 2

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Let $y(x)$ be the solution curve of the differential equation

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The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$ , where m is arbitrary constant, is

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Match List-I with List-II:

List-I	List-II
Differential Equations	Degree/Order
(A) Degree of the differential equation $\frac{d^3y}{dx^3} + 2 \log x.y = 0$	(I) 3
(B) Order of the differential equation $\frac{d^4y}{dx^4} + \left(\frac{dy}{dx}\right)^4 + xy = 0$	(II) 2
(C) Degree of the differential equation $\left(\frac{d^4y}{dx^4}\right)^2 + \left(\frac{dy}{dx}\right)^3 + x^2y = 0$	(III) 1
(D) Order of the differential equation $\frac{d^3y}{dx^3} + y\left(\frac{dy}{dx}\right)^3 = 0$	(IV) 4