Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Ordinary Differential Equations First order Differential Equation
Let y(x) be the solution of the differential equation
\(\frac{d y}{d x}=1+y \sec x \quad \text { for } x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
that satisfies y(0) = 0. Then, the value of y \(\left(\frac{\pi}{6}\right) \) equals
1
\(\sqrt{3} \log \left(\frac{3}{2}\right) \)
2
\(\left( \frac {\sqrt{3}}{2} \right) \log \left(\frac{3}{2}\right) \)
3
\(\left(\frac{\sqrt{3}}{2}\right) \log 3 \)
4
\(\sqrt{3} \log 3\)