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GATE 2020 MT – Question 11

Engineering Mathematics · Differential equations · 1 mark · Multiple choice

The homogeneous ODE $d^2y/dt^2+4dy/dt+3y=0$ has general solution $y=C_1e^{R_1t}+C_2e^{R_2t}$. Find R₁ and R₂.

  1. −1 and −3
  2. −3 and −3
  3. 1 and −3
  4. 1 and 3

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Correct answer: (A) −1 and −3

Explanation

Use a trial solution $e^{Rt}$. Its characteristic equation is $R^2+4R+3=(R+1)(R+3)=0$. The distinct roots −1 and −3 generate the two independent exponential terms, so A gives the required pair.

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