CUET UG 2025 — Mathematics Algebra

A differential equation of order $n$n has a general solution containing $n$n arbitrary constants.

Given differential equation has order $= 4$=4

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

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A particular solution is obtained by assigning specific values to all arbitrary constants in the general solution.

For example:
General solution: $y = C_1e^x + C_2e^{-x} + C_3\sin(x) + C_4\cos(x)$y=C1​ex+C2​e−x+C3​sin(x)+C4​cos(x)

Particular solution: $y = 2e^x + 3e^{-x} + \sin(x) + 5\cos(x)$y=2ex+3e−x+sin(x)+5cos(x)

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After assigning specific values to all constants, no arbitrary constants remain in the particular solution.

Number of arbitrary constants in particular solution $= 0$=0

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The degree of the differential equation (which is 3 in this problem) does not affect the number of arbitrary constants.

Therefore, the number of arbitrary constants in the particular solution is $0$0.