- #1
jhast1
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Homework Statement
I need to integrate dx/dt=k(a-x)(b-x) and then rearrange to find x
The Attempt at a Solution
1/((a-x)(b-x))dx = k dt
Integrating dx using partial fractions:
1/(b-a)×(ln((a-x)/(b-x))=kt+c
when t=0 x=0
∴c=(ln(a/b))/(b-a)
then when I rearrange I get:
x=(e^((b-a)(kt+c))×(a-b))/((e^((b-a)(kt+c))-1)
Then I change the x to y and t to x so that I can graph it, but it doesn't give me the curve that I want, I have attached the graph. I am was assuming that it would give something like the black curve rather than the red one that it gave. Am I doing something wrong?
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