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GATE 2020 CE (CE1) – 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 $x^{\prime\prime}-5x^\prime+6x=0$ with x(0) = 0 and $x^\prime(0)=10$.

  1. $x=-5e^{2t}+6e^{3t}$
  2. $x=5e^{2t}+6e^{3t}$
  3. $x=-10e^{2t}+10e^{3t}$
  4. $x=10e^{2t}+10e^{3t}$

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Correct answer: (C) $x=-10e^{2t}+10e^{3t}$

Explanation

Characteristic roots are 2 and 3. Write $x=Ae^{2t}+Be^{3t}$. Initial conditions give $A+B=0$ and $2A+3B=10$, hence A = −10 and B = 10. **$x=-10e^{2t}+10e^{3t}$, C**.