Diff.Eq. Seperation of variables.

[Jtechguy21]

Homework Statement

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

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

Homework Equations

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

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)+cI have no idea what to do now with the y(0)=0
That means plus in x=0 for the equation correct?

 

[SteamKing]

You use the initial condition to determine the value of c.

when x = 0, y = 0.

 

[Jtechguy21]

You use the initial condition to determine the value of c.

when x = 0, y = 0.

How did you get y=0?

 

[pasmith]

How did you get y=0?

That's what $y(0) = 0$ means!

 

[ChrisVer]

well still there is a problem if x(0) is not zero for y(0)=0...
In that case you solve c with respect to x(0) (a parameter) and input it

 

[Jtechguy21]

okay thank you.
My last question is.
can someone please check my integration
∫Dy/(e^-y +1)=ln|e^-y+1|+y

to make sure ^ is correct?

 

[ChrisVer]

you can always try to take the derivative of the righthand side and check by yourself ;) much easier