Project ForgeEngineering Mathematics
Calculus
GATE 2021
Medium
If y(x) satisfies the differential equation (sin x)(dy/dx) + y cos x = 1, subject to the condition y(π/2) = π/2, then y(π/6) is
- A0
- Bπ/6
- π/3
- Dπ/2
Explanation
The left side is exactly d/dx(y sin x) = y' sin x + y cos x. So d/dx(y sin x) = 1, giving y sin x = x + C. At x=π/2: y=π/2, sin(π/2)=1, so π/2 = π/2 + C, C=0. Thus y = x/sin x. At x=π/6: y = (π/6)/(1/2) = π/3.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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