CUET UG 2025 — Mathematics Calculus

For a differential equation:

Order = The highest derivative in the equation

Degree = The power of the highest order derivative (after removing fractions/radicals)

In this problem:

• Order = 4 (contains fourth derivative $\frac{d^4y}{dx^4}$dx4d4y​)
• Degree = 1 (fourth derivative appears to power 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 constants.

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For this differential equation:

Order = 4

Therefore, number of arbitrary constants = 4

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When solving a differential equation of order 4, integration is performed 4 times:

• First integration introduces constant $C_1$C1​
• Second integration introduces constant $C_2$C2​
• Third integration introduces constant $C_3$C3​
• Fourth integration introduces constant $C_4$C4​

The general solution contains 4 arbitrary constants: $C_1, C_2, C_3, C_4$C1​,C2​,C3​,C4​

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Number of arbitrary constants = 4