Which of the following is the solution to the differential equation dy/dx=ycosx with the initial condition y(pi/2)=e

Question

Which of the following is the solution to the differential equation dy/dx=ycosx with the initial condition y(pi/2)=e

Answer 1

To solve dy/dx=ycosx use separation of variables to get dy/y =cosxdx. Hence lny = sinx + C or y =Ce^sinx. Using the initial condition that y(pi/2) =e then e= Ce or C=1. The equation becomes y= e^sinx as the solution.