The integrating factor of the differential equation xdy/dx - y = 2x^2 is : Option 1: x Option 2: 1/x Option 3: e^(-x) Option 4: e^x

Answer: 1/x. Solution: Rewrite: dy/dx - 1/xy = 2x. Here P(x) = -1/x. IF = e^( -1/xdx) = e^(- x) = 1/x.

Calculus

Differential Equations

Easy

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

$x$

$\frac{1}{x}$

$e^{-x}$

$e^x$

✅ Correct Option: 2

Rewrite: $\frac{dy}{dx} - \frac{1}{x}y = 2x$ . Here $P(x) = -\frac{1}{x}$ . IF $= e^{\int -\frac{1}{x}dx} = e^{-\log x} = \frac{1}{x}$ .

2026: 30 May Shift 2

The particular solution of the differential equation $\sec^2x\tan y\,dx - \sec^2y\tan x\,dy = 0$ , $y=\frac{\pi}{4}$ when $x=\frac{\pi}{4}$ , is

2026: 22 May Shift 1

The particular solution of the differential equation $\log\left(\frac{dy}{dx}\right)=3x+4y$ , given that $y=0$ , when $x=0$ is:

2022: 23 Aug Shift 1

Match List - I with List - II

List - I (Differential Equation)	List - II (Degree)
A. $\left[1 + (y')^2\right]^2 = y''$	I. $2$
B. $\left[1 + (y'')^3\right]^{\frac{1}{2}} = (y')^3$	II. $4$
C. $(y''')^2 + y'' + 3y' + 5y = e^x$	III. $1$
D. $\left[1 + (y')^3\right]^{\frac{1}{2}} = (y'')^2$	IV. $3$

Choose the correct answer from the option given below:

2026: 29 May Shift 2

The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is

2025: 15 May Shift 2

Consider the curve which is represented by the differential equation $\frac{dy}{dx} = 1 + x + y + xy$ . If it passes through the point $(0,0)$ , then which of the following is/are true?

(A) it is a straight line.

(B) it is a parabola.

(D) Its equation is $xy(x + 1)\left(y - \frac{1}{\sqrt{e}} + 1\right) = 0$

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
Differential equation	Degree
(A) $\frac{d^2y}{dx^2} + \sqrt{\frac{dy}{dx}} - y = 0$	(I) 6
(B) $\sqrt{\frac{d^3y}{dx^3}} - \sqrt[12]{\frac{d^2y}{dx^2}} = 0$	(II) Not defined
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} + e^{\frac{dx}{dx}} = x^2$	(III) 3
(D) $\sqrt[3]{\frac{dy}{dx}} - \frac{d^2y}{dx^2} = e^x$	(IV) 2

Choose the correct answer from the options given below:

The integrating factor of the differential equation xdydx−y=2x2x\frac{dy}{dx} - y = 2x^2xdxdy​−y=2x2 is :

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :