MathematicsMedium38×since 2002Q3643Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation dydx=(tanx)+ysinx(secx−sinxtanx),x∈(0,π2)\frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}, x \in\left(0, \frac{\pi}{2}\right)dxdy=sinx(secx−sinxtanx)(tanx)+y,x∈(0,2π) satisfying the condition y(π4)=2y\left(\frac{\pi}{4}\right)=2y(4π)=2. Then, y(π3)y\left(\frac{\pi}{3}\right)y(3π) isA3(2+loge3)\sqrt{3}\left(2+\log _e 3\right)3(2+loge3)B3(1+2loge3)\sqrt{3}\left(1+2 \log _e 3\right)3(1+2loge3)C3(2+loge3)\sqrt{3}\left(2+\log _e \sqrt{3}\right)3(2+loge3)D32(2+loge3)\frac{\sqrt{3}}{2}\left(2+\log _e 3\right)23(2+loge3)Check answerSkip