+267 I stumbled upon the following differential equation:
\(y'=k_1(k_2-y)y\)
I've never encountered a squared function before so I'm kind of stumped on how to proceed with this. I tried putting the following into Wolfram Alpha:
\(\mathscr{L} \{(f(t))^2 \}\)
Which gave me the following error:
(no result found in terms of standard mathematical functions)
So I could use some help with that as Googling didn't give me what I was looking for. On the topic I was also curious about rules for laplace transform of two functions multiplied, I know that the laplace transform is a linear operator but maybe if there's some sort of general rule that applies here:
\(\mathscr{L} \{f(t) \cdot g(t) \}\)
I'm not expecting someone to spoonfeed me too much here but a pointer to some site or pdf/book would be nice. I'm not the most informed on Laplace Transforms though, so try to keep it somewhat simple :) Thanks
Why Laplace Transforms ? Are you required to use this method for some reason ?
The natural method to use is a separation of variables.
\(\displaystyle \frac{dy}{dt}=k_{1}(k_{2}-y)y\), so, \(\displaystyle \frac{dy}{(k_{2}-y)y}=k_{1}dt\).
Split the lhs into partial fractions,
\(\displaystyle \frac{1}{k_{2}y}+\frac{1}{k_{2}(k_{2}-y)}\)
and integrate on both sides.
Tiggsy.
