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GATE 2020 EC – Question 14

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

The general solution of $\dfrac{d^2y}{dx^2}-6\dfrac{dy}{dx}+9y=0$ is

  1. $y=C_1e^{3x}+C_2e^{-3x}$
  2. $y=(C_1+C_2x)e^{-3x}$
  3. $y=(C_1+C_2x)e^{3x}$
  4. $y=C_1e^{3x}$

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Show answer and explanation

Correct answer: (C) $y=(C_1+C_2x)e^{3x}$

Explanation

The characteristic equation $m^2-6m+9=(m-3)^2=0$ has the repeated root $m=3$, so the general solution is $y=(C_1+C_2x)e^{3x}$.