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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