The particular solution of the differential equation (dy/dx)= 3x + 4y satisfying y = 0 when x = 0 is: Option 1: 3e³ˣ + 4e⁻⁴ʸ + 7 = 0 Option 2: 3e³ˣ - 4e⁻⁴ʸ - 7 = 0 Option 3: 4e³ˣ + 3e⁻⁴ʸ - 7 = 0 Option 4: 4e³ˣ - 3e⁻⁴ʸ + 7 = 0

The answer is '4e³ˣ + 3e⁻⁴ʸ - 7 = 0'. View full solution:

CUET Mathematics 2025 - The particular solution of the differential equation (dy/dx)= 3x + 4y satisfying y = 0 when x = 0 is: | PYQs + Solutions

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:

2026: 12th May Shift 2

Match List-I with List-II

List-I (Differential Equation)	List-II (Order and degree)
(A) $\left(\dfrac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 0$	(I) order = 2, degree = 1
(B) $xy\dfrac{d^2y}{dx^2} + x\left(\dfrac{dy}{dx}\right)^2 - y\dfrac{dy}{dx} = 0$	(II) order = 2, degree = not defined
(C) $\left(\dfrac{d^3y}{dx^3}\right)^2 + \log_e\left(\dfrac{dy}{dx}\right) = 4x$	(III) order = 3, degree = 2
(D) $\dfrac{d}{dx}\left(\dfrac{d^2y}{dx^2}\right) + y\dfrac{dy}{dx} = \left(1+\dfrac{dy}{dx}\right)^{1/2}$	(IV) order = 3, degree = not defined

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2025: 21 May Shift 1

The number of arbitrary constants in the general solution of a differential equation with degree 1 and order 3, is

2025: 30 May Shift 1

The differential equation representing the family of curves $y = Ax + \frac{B}{x}$ , $x \neq 0$ where A and B are arbitrary constants, is given by

2026: 31st May Shift 2

Match the LIST-I with LIST-II

[ $a$ is an arbitrary constant]

	LIST-I Differential Equation		LIST-II Family of curves
A.	$x\,dy - y\,dx = 0$	I.	$x^2 + y^2 = a^2$
B.	$2y\,dx - x\,dy = 0$	II.	$y = ax$
C.	$x\,dx + y\,dy = 0$	III.	$y^2 = 16x + a$
D.	$y\,dy - 8\,dx = 0$	IV.	$x^2 = ay$

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2025: 14 May Shift 1

Consider the differential equation, $x\frac{dy}{dx} = y(\log_e y - \log_e x + 1)$ , then which of the following are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(C) Its general solution is $\log_e\left(\frac{y}{x}\right) = Cx$ , where C is constant of integration

(D) Its general solution is $\log_e\left(\frac{x}{y}\right) = Cy$ , where C is constant of integration

(E) If $y(1) = 1$ , then its particular solution is $y = x$

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

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