# differential equation problem

• Feb 19th 2009, 08:48 PM
swimmergirl
differential equation problem
I'm not quite sure how to solve this problem. I tried one step but don't know what to do next. It seems weird.

dw/dt=-lambdaW(t) with W(0)=Winitial

All I did was separate:

dw/-lambdaW(t)=dt but don't now what to do from here because I don't know what W(t) is.

Can anyone help? I will deeply appreciate it! thank you!
• Feb 20th 2009, 12:40 AM
CaptainBlack
Quote:

Originally Posted by swimmergirl
I'm not quite sure how to solve this problem. I tried one step but don't know what to do next. It seems weird.

dw/dt=-lambdaW(t) with W(0)=Winitial

All I did was separate:

dw/-lambdaW(t)=dt but don't now what to do from here because I don't know what W(t) is.

Can anyone help? I will deeply appreciate it! thank you!

Do you mean:

$\frac{dw}{dt}=-\lambda w$ ?

CB
• Feb 20th 2009, 12:49 AM
swimmergirl
the problem in the book says what i originally wrote but i guess it makes sense to write it just as W instead of W(t)
• Feb 20th 2009, 03:01 AM
CaptainBlack
Quote:

Originally Posted by swimmergirl
the problem in the book says what i originally wrote but i guess it makes sense to write it just as W instead of W(t)

Then the solution is:

$\int \frac{1}{w} \ dw=- \lambda \int \ dt$

with the initial condition determining the constant of integrations.

CB