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GATE 2020 AG – Question 13

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Find the general solution of $y\prime\prime\prime-6y\prime\prime+11y\prime-6y=0$.

  1. $C_1e^{-x}+C_2e^{-2x}+C_3e^{-3x}$
  2. $C_1e^{-x}+C_2e^{-2x}+C_3e^{3x}$
  3. $C_1e^{-x}+C_2e^{2x}+C_3e^{3x}$
  4. $C_1e^x+C_2e^{2x}+C_3e^{3x}$

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Correct answer: (D) $C_1e^x+C_2e^{2x}+C_3e^{3x}$

Explanation

The characteristic polynomial factors as (r−1)(r−2)(r−3). Three distinct real roots therefore produce independent solutions eˣ,e²ˣ,e³ˣ. Their arbitrary linear combination is D.

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