Integrating factor of the differential equation x(x-1)dy/dx-(x-2)y=x^3(2x-1), x>1 is: Option 1: (x+1)/x^2 Option 2: (1-x)/x^2 Option 3: (x-1)/x^2 Option 4: (x-1)/x

Answer: (x-1)/x^2. Solution: In standard form, dy/dx-(x-2)/(x(x-1))y=(x^2(2x-1))/(x-1). Since (x-2)/(x(x-1))=2/x-1/(x-1), we get P dx=-2 x+(x-1), so IF=(x-1)/x^2.

Calculus

Differential Equations

Medium

core

Integrating factor of the differential equation $x(x-1)\frac{dy}{dx}-(x-2)y=x^3(2x-1), x>1$ is:

$\frac{x+1}{x^2}$

$\frac{1-x}{x^2}$

$\frac{x-1}{x^2}$

$\frac{x-1}{x}$

✅ Correct Option: 3

In standard form, $\frac{dy}{dx}-\frac{x-2}{x(x-1)}y=\frac{x^2(2x-1)}{x-1}$ .

Since $\frac{x-2}{x(x-1)}=\frac{2}{x}-\frac{1}{x-1}$ , we get $\int P\,dx=-2\log x+\log(x-1)$ , so $IF=\frac{x-1}{x^2}$ .

2025: 26 May Shift 2

The solution of the differential equation $xdy - ydx = 0$ represents

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: 21 May Shift 2

The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

2026: 31 May Shift 2

If $m$ and $n$ are respectively order and degree of the differential equation

$\left(\dfrac{d^2y}{dx^2}\right)^5 + 6\cdot\dfrac{\left(\dfrac{d^2y}{dx^2}\right)^3}{\dfrac{d^3y}{dx^3}} + \dfrac{d^3y}{dx^3} = x^2+5$ then :

2025: 13 May Shift 1

Match List-I with List-II

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

Choose the correct answer from the options given below:

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Sum of the order and the degree of the differential equation
A.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$	I.	$2$
B.	$4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$	II.	$3$
C.	$x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$	III.	$5$
D.	$\dfrac{dy}{dx} = x^4 e^{-3y}$	IV.	$4$

Choose the correct answer from the options given below:

Integrating factor of the differential equation x(x−1)dydx−(x−2)y=x3(2x−1),x>1x(x-1)\frac{dy}{dx}-(x-2)y=x^3(2x-1), x>1x(x−1)dxdy​−(x−2)y=x3(2x−1),x>1 is:

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CUET Mathematics Past Year Questions (Topic-Wise)

Integrating factor of the differential equation $x(x-1)\frac{dy}{dx}-(x-2)y=x^3(2x-1), x>1$ is: