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Single Variable Calculus

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Separable Equation with the Secant Function

SVCALC-R7JQPH

Solve the following differential equation where $y(0)=\pi/2$ and determine the interval of validity for the solution.

$$ \frac{dy}{dx}=\frac{1}{2} \sec y$$

A

$y =\arcsin \left( \frac{x}{2} +1 \right), \,\, -4 \leq x \leq 0$

B

$y =\arcsin \left( \frac{x}{2} +1 \right), \,\, x \mbox{ all real numbers}$

C

$y =\arccos \left( \frac{x}{2} +1 \right), \,\, -4 \leq x \leq 0$

D

$ y =\arcsin \left( \frac{x}{2} -1 \right), \,\, 0 \leq x \leq 4$