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GATE 2019 ME (ME2) – Question 13

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 1 mark · Multiple choice

The differential equation $dy/dx+4y=5$ holds on $0\le x\le1$, with y(0) = 2.25. Find its solution.

  1. $y=e^{-4x}+5$
  2. $y=e^{-4x}+1.25$
  3. $y=e^{4x}+5$
  4. $y=e^{4x}+1.25$

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Correct answer: (B) $y=e^{-4x}+1.25$

Explanation

The particular solution is $5/4=1.25$ and homogeneous solution is $Ce^{-4x}$. Initial condition gives $C=2.25-1.25=1$. Thus **$y=e^{-4x}+1.25$, B**.