The differential equation of the family of curves y = Ae^3x + Be^-3 x, where a and are arbitrary constants, is Option 1: d^2y/dx^2 + 9y = 0 Option 2: d^2y/dx^2 + 3y = 0 Option 3: d^2y/dx^2 = 9y Option 4: d^2y/dx^2 = 3y

The answer is 'd^2y/dx^2 = 9y'. View full solution:

CUET Mathematics 2025 - The differential equation of the family of curves y = Ae^3x + Be^-3 x, where a and are arbitrary constants, is | PYQs + Solutions

2023: 23 May Shift 3

The general solution of $\frac{dy}{dx} = 1 + x^2 + y^2 + x^2y^2$ is:

(given that $C$ is the constant of integration)

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: 22nd May Shift 2

For a given differential equation $e^{dy/dx} = x + 1; x \in (-1,\infty)$ , then which of the following statements are TRUE?

(A) Its general solution is $y = x\log_e(x+1) - x + \log_e(x+1) + C$ ; C is an arbitrary constant.

(B) Its particular solution is $y = (x+1)\log_e(x+1) - x + 5; y(0) = 5$

(C) Its general solution is $y = (x-1)\log(x+1) - x + C$ ; C is an arbitrary constant

(D) Its particular solution is $y = (x-1)\log(x+1) - x + 5; y(0) = 5$

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2025: 15 May Shift 1

Match List-I with List-II

List-I	List-II
(Differential equation)	(Order and Degree)
(A) $\frac{d^3y}{dx^3} + y^2 + e^{dy/dx} = 0$	(I) order = 3, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} + 1 = 0$	(II) order = 3, degree not defined
(C) $2x^2\frac{d^2y}{dx^2} - 3\left(\frac{dy}{dx}\right)^2 + y = 0$	(III) order = 2, degree = 3
(D) $\frac{d^3y}{dx^3} + 2\left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$	(IV) order = 2, degree = 1

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2025: 21 May Shift 1

The general solution of the differential equation $x(1 + y^2)dx + y(1 + x^2)dy = 0$ is

2026: 29th May Shift 2

Match the LIST-I with LIST-II

	LIST-I Differential equations		LIST-II Integrating factor
A.	$(x+y)\dfrac{dy}{dx} = 1$	I.	$e^{-x}$
B.	$x\dfrac{dy}{dx} - y = x^2$	II.	$x$
C.	$\dfrac{dy}{dx} - y = \sin x$	III.	$\dfrac{1}{x}$
D.	$x\dfrac{dy}{dx} + y = \tan x$	IV.	$e^{-y}$

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