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GATE 2016 EC (EC3) – Question 36

Engineering Mathematics · Differential Equations · 2 marks · Multiple choice

The initial-value problem $y^{\prime\prime}+12y\prime+36y=0$, $y(0)=3$, $y\prime(0)=-36$ has solution

  1. $(3-18x)e^{-6x}$
  2. $(3+25x)e^{-6x}$
  3. $(3+20x)e^{-6x}$
  4. $(3-12x)e^{-6x}$

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Correct answer: (A) $(3-18x)e^{-6x}$

Explanation

The characteristic polynomial is $(r+6)^2$, giving $y=(C_1+C_2x)e^{-6x}$. From y(0)=3, C1=3.

Differentiate and evaluate at zero: $y\prime(0)=C_2-6C_1=C_2-18=-36$. Thus C2=−18.

The required solution is **$(3-18x)e^{-6x}$, A**.

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