If and , find an equation for in terms of…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

2. If sec⁡xdydx=4tan⁡y\sec x \frac{d y}{d x}=4 \tan y and y(0)=π6y(0)=\frac{\pi}{6}, find an equation for yy in terms of xx. (A) sec⁡2y=32e4sin⁡x\sec ^{2} y=\frac{\sqrt{3}}{2} e^{4 \sin x} (B) sec⁡2y=12e4sin⁡x\sec ^{2} y=\frac{1}{2} e^{4 \sin x} (C) sin⁡y=32e4sin⁡x\quad \sin y=\frac{\sqrt{3}}{2} e^{4 \sin x} (D) sin⁡y=12e4sin⁡x\quad \sin y=\frac{1}{2} e^{4 \sin x}

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