A Level MathsWatch
The question asks me to solve it expressing x in terms of k and t.
I've got to this far:
dx = kx (1-x) dt
1/x(1-x) dx = k dt
Put integral signs in and then integrate the left side using partial fractions to get:
ln(x) - ln(x-1)
Putting it all together:
ln(x)- ln(x-1) = 1/2 k^2 +c
What would I do know? The question asks to express x in terms of k and t?
subtract logs then raise both sides to the power of e, make x the subject