Question

Let 𝑦(𝑥) be the solution of the differential equation
\(\frac{dy}{dx}=1+y\sec x\ \ \text{for}\ x \in(-\frac{\pi}{2},\frac{\pi}{2})\)
that satisfies 𝑦(0) = 0. Then, the value of \(y(\frac{\pi}{6})\) equals

• A. \(\sqrt3\ \log(\frac{3}{2})\)
• B. \((\frac{\sqrt3}{2}) \log(\frac{3}{2})\)
• C. \((\frac{\sqrt3}{2}) \log 3\)
• D. \(\sqrt3 \log 3\)

Answer 1

The Correct Option is A

The correct option is (A) : \(\sqrt3\ \log(\frac{3}{2})\).