Ignoring the second part of the question for now, since I think it will be more clear once I understand how this equation is homogeneous.
According to my textbook and online resources a first-order ODE is homogeneous when it can be written like so:
$$M(x,y) dx + N(x,y) dy = 0$$
and ##M(x,y)##...
Yes, in fact having recently re-done the math with the more correct formula for initial Ca-48 mass
$$N_1 = \frac {φ σ N_0 (1 - e^{-λt})} {λ}$$
Gives me a mass of Ca-48 of 36.8g, far too large to be 0.2% of anything with a maximum of 50g.
I'm honestly beginning to think there's a typo in the...
I think I have the answer, but when I calculate it out, I'm off by at least an order of magnitude.
My process goes like this:
The (looked up) specific activity of Ca-49 is ##1.63*10^7 TBq/g##, which is ##1.63*10^{16} KBq/g##
The activity of the sample after 5 minutes rest is ##166KBq##, per...
The vector equation is ## v(x)=(e^x cos(2x), e^x sin(2x), e^x) ##
I know the arc-length formula is ## S=\int_a^b \|v(x)\| \,dx ##
I found the derivative from a previous question dealing with this same function, but the when I plug it into the arc-length function I get an integral that I've...