The differential equation representing family of curves y = ae^mx + be^nx, where a and b are arbitrary constants, is Option 1: d^2y/dx^2 + (m+n)dy/dx + y = 0 Option 2: d^2y/dx^2 + mndy/dx + (m+n)y = 0 Option 3: d^2y/dx^2 - (m+n)dy/dx + mny = 0 Option 4: d^2y/dx^2 + (m+n)dy/dx - mny = 0

The answer is 'd^2y/dx^2 - (m+n)dy/dx + mny = 0'. View full solution:

CUET Mathematics - The differential equation representing family of curves y = ae^mx + be^nx, where a and b are arbitrary constants, is | PYQs + Solutions

CUET Mathematics 2022 10 Aug Shift 1

Calculus

Medium

$\frac{d^2y}{dx^2} + (m+n)\frac{dy}{dx} + y = 0$

$\frac{d^2y}{dx^2} + mn\frac{dy}{dx} + (m+n)y = 0$

$\frac{d^2y}{dx^2} - (m+n)\frac{dy}{dx} + mny = 0$

$\frac{d^2y}{dx^2} + (m+n)\frac{dy}{dx} - mny = 0$

✅ Correct Option: 3

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List-I	List-II
(A) Degree of the differential equation $\frac{d^2y}{dx^2} = e^{dy/dx}$ is	(I) 2
(B) Order of the differential equation $(\frac{dy}{dx})^2 + \frac{d^3y}{dx^3} = 0$ is	(II) not defined
(C) Degree of the differential equation $\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 - 5x^2 = 0$	(III) 3
(D) If p is the order and q is the degree of the differential equation $\frac{dy}{dx} + 3y = e^x$ , then p + q is	(IV) 1

Choose the correct answer from the options given below:

CUET Mathematics 2022 10 Aug Shift 1 PYQs

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