Differential Equations without numbers

[Colts]

Homework Statement

Here is the whole problem.

Homework Equations

Not sure

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)?

 

[Dick]

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

 

[Colts]

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

 

[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 into the equation I got. Once I solve for B I put it in the equation at part a. and solving for A.

 

[HallsofIvy]

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.

 

[Dick]

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

 

[Colts]

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

I got it, Thank you!