The solution of the differential equation {d^{3}y}/{dx^{3}}−5.5 {d^{2}y}/{dx^{2}} + 9.5\frac{dy}{dx}−5y = 0 is expressed as 𝑦 = 𝐶 1 𝑒 2.5𝑥 + 𝐶 2 𝑒 𝛼𝑥 + 𝐶 3 𝑒 𝛽𝑥 , where 𝐶 1 , 𝐶 2 , 𝐶 3 , 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?

GATE Civil Engineering (CE) 2023 Shift 2 Solved Paper

Question : 36 of 65

Marks: +1, -0

The solution of the differential equation

\;{d^{3}y}/{dx^{3}}−5.5\;{d^{2}y}/{dx^{2}} + 9.5\;{dy}/{dx}−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

Validate

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