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

Answer: (A)

$\sqrt3\ \log(\frac{3}{2})$

Answer 2

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