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GATE 2020 CE (CE2) – Question 36

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 2 marks · Multiple choice

Solve $6y^{\prime\prime}+y^\prime-y=0$ in constants $C_1,C_2$.

  1. $y=C_1e^{-x/3}+C_2e^{x/2}$
  2. $y=C_1e^{x/3}+C_2e^{-x/2}$
  3. $y=C_1xe^{-x/3}+C_2e^{x/2}$
  4. $y=C_1e^{-x/3}+C_2xe^{x/2}$

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Correct answer: (B) $y=C_1e^{x/3}+C_2e^{-x/2}$

Explanation

The characteristic equation is $6r^2+r-1=(3r-1)(2r+1)=0$. Roots are 1/3 and −1/2. Thus **$y=C_1e^{x/3}+C_2e^{-x/2}$, B**.