# 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.

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