If-y-x-is-a-solution-of-the-differential-equation-2-sinx-1-y-dy-dx-cosx-and-y-0-1-then-find-the-value-of-y-pi-2-

Question Number 77297 by vishalbhardwaj last updated on 05/Jan/20

If y(x) is a solution of the differential equation (((2+sinx)/(1+y)))(dy/dx)=−cosx and y(0)=1, then find the value of y(π/2) ?

$$\mathrm{If}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\left(\frac{\mathrm{2}+\mathrm{sinx}}{\mathrm{1}+\mathrm{y}}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{cosx}\:\mathrm{and} \\ $$$$\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{y}\left(\pi/\mathrm{2}\right)\:\:? \\ $$

Answered by john santu last updated on 05/Jan/20