Calculus

Differential Equations

Easy

common

Which of the following differential equations has $y = x$ as one of its particular solution?

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

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

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

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

✅ Correct Option: 2

For $y=x$ we have $y'=1$ and $y''=0$ .

Substituting in option 2: $0 - x^2(1) + x(x) = 0$ , which matches the right side. The other options give nonzero mismatches, so option 2 is satisfied.

2026: 21 May Shift 1

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$ ; $y(0)=5$ is

2025: 3 June Shift 1

Consider the differential equation $xdy = (y + 2x^3)dx$ . Then which of the following are TRUE?

(A) It is a homogeneous differential equation.

(B) Product of the order and degree of the differential equation in one.

(D) General solution of the differential equation is $y = x^3 + Cx$ , where C is an arbitary constant.

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:

2026: 29 May Shift 2

The solution of the differential equation $\frac{dy}{dx} + y = 1, y(1) = 0$ is

2025: 30 May Shift 2

The sum of order and degree of the differential equation $y = x\frac{dy}{dx} + 2\sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ is

Which of the following differential equations has y=xy = xy=x as one of its particular solution?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which of the following differential equations has $y = x$ as one of its particular solution?