# Seperable DE Help!!

• Feb 23rd 2010, 12:21 PM
calculuskid1
Seperable DE Help!!
I have a DE of Ds/Dt=(5-s)/50 S(0)=0
I keep doing it wrong and it is very frustrating I do not know why. I know how to do it and everything but I must keep plugging in numbers wrong
• Feb 23rd 2010, 12:25 PM
icemanfan
This is a separable DE. You have

$\frac{ds}{dt} = \frac{5-s}{50}$

$\frac{ds}{5-s} = 50 \cdot dt$

$\int \frac{ds}{5-s} = \int 50 \cdot dt$.

How far have you gone past this point? What are you having trouble with?
• Feb 23rd 2010, 12:40 PM
calculuskid1
I think my biggest problem is I dont know what is going on here:
how does
-ln (5-s)=1/50t-ln5the same as
ln(5/5-s)=1/50t
• Feb 23rd 2010, 01:24 PM
Ted
Quote:

Originally Posted by icemanfan
This is a separable DE. You have

$\frac{ds}{dt} = \frac{5-s}{50}$

$\frac{ds}{5-s} = \color{red} 50 \cdot dt$

Its $\frac{ds}{5-s}=\frac{1}{50}dt$.