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GATE 2021 ME (ME1) – Question 11

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

If $y(x)$ satisfies the differential equation $\frac{dy}{dx}\sin x+y\cos x=1$, subject to the condition $y(\pi/2)=\pi/2$, then $y(\pi/6)$ is

  1. 0
  2. $\pi/6$
  3. $\pi/3$
  4. $\pi/2$

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Show answer and explanation

Correct answer: (C) $\pi/3$

Explanation

The left side is the product derivative $(y\sin x)^{\prime}$. Integrating gives y sin x=x+C. At π/2 the initial condition gives C=0.

Therefore $y(\pi/6)=(\pi/6)/(1/2)=\mathbf{\pi/3}$, **C**.