Quick differntial equation question

demon8991 · 9 Jun 2007 at 17:46

d θ
--- = -K (θ-20)
d t

Determine whether or not the differential equations may be solved by using any one or all of the following methods;

a)Direct Integration
b)Separating the variables
c)Integrating factor

Just to double check myself, which of these will work with the equation?

Millwall.FC · 9 Jun 2007 at 17:48

defantly E :eek:

p4radox · 9 Jun 2007 at 18:12

edit: I'll shut up I think I'm talking rubbish.

Arcade Fire · 9 Jun 2007 at 18:13

(a) To solve an equation by direct integration you have to be able to integrate every term. You can integrate the left-hand side, and you can integrate the constant on the right-hand side, but what about the other term.

(b) Edit: Apparently 'separate variables' has a different meaning at A Level than the one I know! In this case you should be able to do it without too much trouble.

(c) Should work - can you see how?

demon8991 · 9 Jun 2007 at 18:51

Brilliant thanks, i thought it was b) anyway. Just wanted to make sure i was right before i solved it.

Dave · 9 Jun 2007 at 20:16

Yeah, assuming K is not a function of theta or t and 20 is a constant, you can separate the variables in order to solve the differential.

Arcade Fire · 9 Jun 2007 at 20:22

Dave said:
Yeah, assuming K is not a function of theta or t and 20 is a constant...

What else would it be?

Dave · 9 Jun 2007 at 20:36

Arcade Fire said:
What else would it be?

I dunno, it might be 2*O, where O is some function of t.

/tries desperately to make up excuse

demon8991 · 9 Jun 2007 at 23:04

Does it give?

ln(theta-20) + kt = 0

DaveF · 10 Jun 2007 at 00:21

demon8991 said:
Does it give?

ln(theta-20) + kt = 0

What happened to your arbitrary constant?

Inquisitor · 10 Jun 2007 at 00:32

demon8991 said:
Does it give?

ln(theta-20) + kt = 0

You missed out the constant of integration. Should be:

θ = je^(-kt) + 20