# Differential Equations without numbers

1. Feb 5, 2013

### Colts

1. The problem statement, all variables and given/known data
Here is the whole problem.

2. Relevant equations
Not sure

3. The attempt at a solution
As you can see I got the first part. I solved the equation at part a.) for A(c) and plugged it into the D.E. and then solved for B(c). I need help on how to do the next part. How do I get B(0)?

2. Feb 5, 2013

### Dick

B(0)=A(0)-L, right?

3. Feb 5, 2013

### Colts

I feel really dumb haha. Thank you, I was thinking they were looking for a number.

4. Feb 5, 2013

### Colts

Now I'm having trouble with part b.

I'm solving dB/dc = -kB by doing it as a separable equation and getting B=sqrt(-2ck+2p) where p is the constant of integration. Then using the IVP of B to find P and plugging it back in to the equation I got. Once I solve for B I put it in the equation at part a. and solving for A.

5. Feb 5, 2013

### HallsofIvy

Staff Emeritus
The square root is clearly NOT a solution. If $B= \sqrt{2p- n2ck}= (2p- 2ck)^{1/2}$ then $dB/dc= (1/2)(-2k)(2p- 2ck)^{-1/2}= -k/B$, not "-kB". Do the integration again.

6. Feb 5, 2013

### Dick

And showing what you are integrating would be helpful as well.

7. Feb 5, 2013

### Colts

I was integrating B dB when I should have been integrating 1/B dB

I got it, Thank you!