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The solution of the differential equation

\(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\)

is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 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?

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GATE CE 2023 Official Paper: Shift 2
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  1. 1 and 2
  2. −1 and −2
  3. 2 and 3
  4. −2 and −3

Answer (Detailed Solution Below)

Option 1 : 1 and 2
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Detailed Solution

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Auxillary equation is,

m3 – 5.5 m2 + 9.5 m – 5 = 0

By solving above equation, we get m = 2.5, 1, 2

So, m1 and m2 are 1 and 2.

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More Partial Differential Equations Questions

Q1.The solution of the differential equation \(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\) is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 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?
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More Differential Equations Questions

Q1.The general solution of the differential equation \(\frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} \) is
Q2.The solution of the differential equation \(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\) is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 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?
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