# solving the differential equation...

• Feb 6th 2010, 05:17 AM
slapmaxwell1
solving the differential equation...
ok here we go...

the rate of change of N with respect to S is proportional to 500 - S

so the set up is pretty straight forward...

I got dN/dS = k(500 - S)

when i integrated it i got N = 500S - (S)^2/2 + C, the book said something different..which is where im confused..

books answer: N = -k/2(500 - S)^2

• Feb 6th 2010, 05:23 AM
HallsofIvy
Quote:

Originally Posted by slapmaxwell1
ok here we go...

the rate of change of N with respect to S is proportional to 500 - S

so the set up is pretty straight forward...

I got dN/dS = k(500 - S)

when i integrated it i got N = 500S - (S)^2/2 + C, the book said something different..which is where im confused..

books answer: N = -k/2(500 - S)^2

Check to see if the problem didn't say
"the rate of change of N with respect to S is inversely proportional to 500 - S".
• Feb 6th 2010, 05:34 AM
slapmaxwell1
ok it said proportional....
• Feb 6th 2010, 06:09 AM
slapmaxwell1
the book says,

dN/ds = k(500 - s)

dN/ds = k(500- s)

∫▒dN/ds ds= ∫▒〖k(500-s)ds〗

∫▒dN= - k/2 (500 - s)^2 + C
N= -k/2 (500-s)^2+C