Hi. I'm new to differential equations; however, I think I see the solution. Check it out:

The idea here is to try and make one side look like the derivative of a product. Take the left side and multiply by the function sec X. Carrying that over the entire equation yields: SecX*y' + secXtanX*y =cosX

This is clearly the deritive of the product secX*y. Simply integrate both sides and get the new equation: secX*y=sinX +c. Just divide by secX and you receive: Y=sinXcosX+cosX