Which of the following differential equations has y=x as one of the particular solution? Option 1: d^2y/dx^2-xdy/dx+xy=x Option 2: d^2y/dx^2+xdy/dx+xy=x Option 3: d^2y/dx^2-x^2dy/dx+xy=0 Option 4: d^2y/dx^2+xdy/dx+xy=0

The answer is 'd^2y/dx^2-x^2dy/dx+xy=0'. View full solution:

CUET Mathematics - Which of the following differential equations has y=x as one of the particular solution? | PYQs + Solutions

CUET Mathematics 2026 12th May Shift 2

Calculus

Medium

core

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

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

$\dfrac{d^2y}{dx^2}-x^2\dfrac{dy}{dx}+xy=0$

$\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}+xy=0$

✅ Correct Option: 3

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Match List-I with List-II

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^2 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^5 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Choose the correct answer from the options given below: