Calculust-2

Calculus Level 5

Solve the differential equation: $\dfrac{dy}{dx} = \dfrac{\tan y}{x+1}+(1+x)e^{x}\sec y$ Given that $y(-0.5) = \sin^{-1}\left(\frac{1}{2}e^{-0.5}\right)$ , what is $y(0)?$

Details and Assumptions:

$y \in \text{[} 0, \frac{\pi}{2} \text{]}$
Give your answer up to $2$ decimal places.