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GATE 2017 CE (CE2) – Question 39

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

For $y^{\prime\prime}-4y^\prime+3y=2t-3t^2$, the particular solution is ______.

  1. $-2-2t-t^2$
  2. $-2t-t^2$
  3. $2t-3t^2$
  4. $-2-2t-3t^2$

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Correct answer: (A) $-2-2t-t^2$

Explanation

Try $y=at^2+bt+c$. Substitution gives $3at^2+(3b-8a)t+(2a-4b+3c)$. Equating coefficients yields $a=-1$, $b=-2$ and $c=-2$. Thus $y_p=-t^2-2t-2$ (A).