Mathematics - Differential Equation Question with Solution | TestHub

If the solution $y(x)$ of the given differential equation $\left({\mathrm{e}}^y+1\right)\cos x\mathrm{d}x+{\mathrm{e}}^y\sin x\mathrm{d}y=0$ passes through the point $\left(\frac{\pi }{2},0\right)$, then the value of ${\mathrm{e}}^{y\left(\frac{\pi }{6}\right)}$ is equal to_________