CUET UG 2025 — Mathematics Calculus

Given:
Order = 3
Degree = 1

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The number of arbitrary constants in the general solution of a differential equation equals the order of the differential equation.

The degree does not affect the number of arbitrary constants.

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Number of arbitrary constants = Order = 3

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When solving a differential equation of order 3, integration is performed 3 times. Each integration introduces one arbitrary constant.

For example, if $\frac{d^3y}{dx^3} = 0$dx3d3y​=0:

First integration: $\frac{d^2y}{dx^2} = C_1$dx2d2y​=C1​

Second integration: $\frac{dy}{dx} = C_1x + C_2$dxdy​=C1​x+C2​

Third integration: $y = \frac{C_1x^2}{2} + C_2x + C_3$y=2C1​x2​+C2​x+C3​

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Therefore, the number of arbitrary constants is 3.