THe answers to the diff eq. are called integral curves...and yes each different C represents a different integral curve...
you said you can answer two
and for the third one start with isoclines take e^(-y)dy/dt+2*cos(t)=0
so ln(e^(-y)dy/dt))=ln(-2cos(t)) and then -y=-ln(y')+ln(-2cos(t)) ...now call y' c...now pick a value for c..say one when c=1 y=-y=-ln(1)+ln(-2cos(t)) =ln(-2cos(t)) and you graph ln(-2cos(t)) and every point on that line will have a direction of 1...now pick more c's and repeat