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Solve the differential equation:dydx=tanyx+1+(1+x)exsecy\dfrac{dy}{dx} = \dfrac{\tan y}{x+1}+(1+x)e^{x}\sec y dxdy=x+1tany+(1+x)exsecy Given that y(−0.5)=sin−1(12e−0.5)y(-0.5) = \sin^{-1}\left(\frac{1}{2}e^{-0.5}\right)y(−0.5)=sin−1(21e−0.5), what is y(0)?y(0)?y(0)?
Details and Assumptions:
y∈[0,π2] y \in \text{[} 0, \frac{\pi}{2} \text{]} y∈[0,2π]
Give your answer up to 222 decimal places.
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