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GATE Civil Engineering (CE) 2023 Shift 2 Solved Paper

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Question : 36

Total: 65

The solution of the differential equation
‌

−5y=0
is expressed as 𝑦 = 𝐶₁𝑒^2.5𝑥 + 𝐶₂𝑒^𝛼𝑥 + 𝐶₃𝑒^𝛽𝑥 , where 𝐶₁, 𝐶₂, 𝐶₃, 𝛼, and 𝛽 are constants, with α and β being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?

1 and 2
−1 and −2
2 and 3
−2 and −3

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