Question

dy/dt = y(1-y)-hy

Suppose that y(0) = y naught > 0
Solve IVP .

Answer 1

separation of variables works...

Answer 2

dy divides through .. but how does that look as integration

Answer 3

\[\int\limits_{ }^{ } \frac{ dy }{ y(1-y-h) } = t+C\]

Answer 4

I simplified a bit.

Answer 5

could you possibly just show me where you simplified?
thats part i'm having trouble with i think

Answer 6

so we're just integrating the function
(y(1-y-h))^-1

Answer 7

right?

Answer 8

yes

Answer 9

which is just ... ln|y(1-y-h)| ?

Answer 10

over h-1?

Answer 11

how's it coming?

Answer 12

hmm... integral du/u = ln(u)
but here, what would you pick for u?
if you pick y(1-y-h), as you did, then du = ?

Answer 13

wait why are we working with du now?

Answer 14

hey!

Answer 15

hey. got it yet?

Answer 16

nooo!!! :( please help

Answer 17

Then from here, apply a Bournoulli Substitution, have you learned that yet? :o