Homework Help: Diff.Eq. Seperation of variables.

1. Feb 25, 2014

Jtechguy21

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?

Last edited: Feb 25, 2014
2. Feb 25, 2014

SteamKing

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

when x = 0, y = 0.

3. Feb 25, 2014

Jtechguy21

How did you get y=0?

4. Feb 25, 2014

pasmith

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

5. Feb 25, 2014

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

6. Feb 25, 2014

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?

7. Feb 25, 2014

ChrisVer

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