Diff.Eq. Seperation of variables.

1. The problem statement, all variables and given/known data

Solve the given differential equation subject to the indicated initial condition.



(e^-y + 1)sinxdx=(1+cosx)d, y(0)=0





2. Relevant equations

Basically we have to use seperation of varaibles to solve before using initial value condition.





3. The attempt at a solution

After separation of variables



Dy/(e^-y +1) = sinx dx/(1+cosx)



take the integral of both sides

∫Dy/(e^-y +1)=ln|e^-y+1|+y



∫sinx dx/(1+cosx)= -ln(1+cosx)+c



Clean it up a bit

ln|e^-y+1|+y= -ln(1+cosx)+c





I have no idea what to do now with the y(0)=0

That means plus in x=0 for the equation correct?