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**Ch 1--2 / 2.5 - Confusion about Population Dynamics Derivation**

« **on:**January 30, 2013, 07:58:54 PM »

In advance, I'm sorry that the way that the following math is done isn't gonna be super pretty, math typing isn't my thing.

Anyways, in Boyce & DiPrima 9 ed. pp. 82 (may be slightly different in 10 ed.), the assertion is made that

y' = ry(1-y/k) simplifies to y = (y

In the middle of the derivation, int([1/K]/[1-y/K]) is presumed to equal -ln(1-y/K)

However,

int((1/K)/(1-y/K))

=int(1/(K-y))

=-ln(K-y)

Plugging this into WolframAlpha also yields the answer -ln(k-y)

What accounts for this discrepancy?

Anyways, in Boyce & DiPrima 9 ed. pp. 82 (may be slightly different in 10 ed.), the assertion is made that

y' = ry(1-y/k) simplifies to y = (y

_{0}K)/(y_{0}+((K-y_{0})e^{-rt})In the middle of the derivation, int([1/K]/[1-y/K]) is presumed to equal -ln(1-y/K)

However,

int((1/K)/(1-y/K))

=int(1/(K-y))

=-ln(K-y)

Plugging this into WolframAlpha also yields the answer -ln(k-y)

What accounts for this discrepancy?