MathematicsMedium38×since 2002Q3553If y=y(x)y=y(x)y=y(x) is the solution curve of the differential equation dydx+ytanx=xsecx,0≤x≤π3,y(0)=1\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1dxdy+ytanx=xsecx,0≤x≤3π,y(0)=1, then y(π6)y\left(\frac{\pi}{6}\right)y(6π) is equal toAπ12−32loge(23e)\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2 \sqrt{3}}{e}\right)12π−23loge(e23)Bπ12+32loge(23e)\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2 \sqrt{3}}{e}\right)12π+23loge(e23)Cπ12+32loge(2e3)\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2}{e \sqrt{3}}\right)12π+23loge(e32)Dπ12−32loge(2e3)\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2}{e \sqrt{3}}\right)12π−23loge(e32)Check answerSkip