Integrating factor of the differential equation x xdy/dx+y=2 x is equal to: (Consider x=_e x) Option 1: x x Option 2: x Option 3: e^x Option 4: 1/x

Answer: x. Solution: Divide by x x to get dy/dx+y/(x x)=2/x. Then IF =e^(/(x x))=e^(, x, )= x.

Calculus

Differential Equations

Medium

core

Integrating factor of the differential equation $x\log x\frac{dy}{dx}+y=2\log x$ is equal to:

(Consider $\log x=\log_e x$ )

$x\log x$

$\log|x|$

$e^x$

$\frac{1}{x}$

✅ Correct Option: 2

Divide by $x\log x$ to get $\frac{dy}{dx}+\frac{y}{x\log x}=\frac{2}{x}$ . Then IF $=e^{\int\frac{dx}{x\log x}}=e^{\log|\log x|}=\log x$ .

2025: 16 May Shift 1

The particular solution of the differential equation x(1 + y²)dx - y(1 + x²)dy = 0, y(0) = 1, is:

2025: 15 May Shift 1

Let $y(x) = a(x + 1) \log(x + 1) + bx + 5$ be the solution of the differential equation e $^\frac{dy}{dx} = x + 1_{;}y(0) = 5$ , then the value of $(a + b)$ is:

2025: 21 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	General solution
---	---
(A) $\dfrac{dy}{dx} = \dfrac{y}{x}; x \neq 0$	(I) $y = cx; c \text{ is an arbitrary constant}$
(B) $x dx - y dy = 0; y \neq 0, x \neq 0$	(II) $x^2 - y^2 = c; c \text{ is an arbitrary constant}$
(C) $\dfrac{(x^2 - 1)}{y^2 + 1}\dfrac{dx}{dy} = 1$	(III) $2x + 3y = c; c \text{ is an arbitrary constant}$
(D) $2 dx + 3 dy = 0$	(IV) $(x^3-y^3) = c + 3(x+y); c \text{ is an arbitrary constant}$

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Sum of order and degree)
A.	$(y'')^3 + xy' + 2y = 0$	I.	$6$
B.	$(y'')^2 + (y')^3 + 4y = 0$	II.	$3$
C.	$y'' + (y')^2 + 5y = 0$	III.	$4$
D.	$(y'')^4 + 3x(y')^2 + y = 0$	IV.	$5$

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

If the solution curve of the differentiable equation $\frac{dy}{dx} + 2y = e^{3x}$ , passes through the point $\left(0, \frac{6}{5}\right)$ , then the value of $y(\log_e 2)$ is:

Integrating factor of the differential equation xlog⁡xdydx+y=2log⁡xx\log x\frac{dy}{dx}+y=2\log xxlogxdxdy​+y=2logx is equal to: (Consider log⁡x=log⁡ex\log x=\log_e xlogx=loge​x)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Integrating factor of the differential equation $x\log x\frac{dy}{dx}+y=2\log x$ is equal to:

(Consider $\log x=\log_e x$ )