The general solution of the differential equation dy/dx = 3e^2x+3e^4xe^x+e^-x is Option 1: y = e^3x + C, where C is arbitrary constant Option 2: y = e^3x3 + C, where C is arbitrary constant Option 3: y = 3e^ex + C, where C is arbitrary constant Option 4: y = e^2x2 + C, where C is arbitrary constant

The answer is 'y = e^3x + C, where C is arbitrary constant'. View full solution:

CUET Mathematics - The general solution of the differential equation dy/dx = 3e^2x+3e^4xe^x+e^-x is | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 2

Calculus

Medium

common

$y = e^{3x} + C$ , where C is arbitrary constant

$y = \frac{e^{3x}}{3} + C$ , where C is arbitrary constant

$y = 3e^{ex} + C$ , where C is arbitrary constant

$y = \frac{e^{2x}}{2} + C$ , where C is arbitrary constant

✅ Correct Option: 1

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The product of order and degree of the differential equation

$x\dfrac{d^3y}{dx^3} = \left(1 + \left(\dfrac{dy}{dx}\right)^2\right)^4$ is

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

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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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