Differential equations (1 Viewer)

[HeeeHeee]

Hi Guys. For part ii do we need to memorize the differential equation general solution
If not how do we solve? Thanks

 

[Masaken]

When I was taught this equation, we were taught how to solve it for fun, but it's quite long (I don't remember if my tutor said to memorise it or not, but my tutor told me it used ext 2 integration, so not sure). I would take a pic of my notes, but as I don't have them right now, here's the solution and how to get it: https://math.libretexts.org/Bookshe...Pdt=rP(1−PK,relative to the carrying capacity.

(Scroll down to 'Solving the Logistic Differential Equation')

 

[pikachu975]

Hi Guys. For part ii do we need to memorize the differential equation general solution
View attachment 35637If not how do we solve? Thanks


View attachment 35636

ii)
Question says "HENCE" meaning you should use part (i).

dP/dt = P/30 * (10000-P)/10000
dP/dt = (1/30) * P(10000-P)/10000
dt/dP = 30 (1/P + 1/(10000-P)) using part (i)

Integrate:
t = 30 lnP - 30 ln(10000-P) + C
At t = 0, P = 1200
C = 30 ln8800 - 30ln1200

t = 30lnP - 30 ln(10000-P) + 30 ln8800 - 30ln1200
t/30 = ln(8800P/1200(10000-P))
e^(t/30) = 22P/3(10000-P)
30000 e^(t/30) - 3P e^(t/30) = 22P
P (22+3e^(t/30)) = 30000 e^(t/30)
P = 30000 e^(t/30) / (22 + 3e^(t/30))

 

[cossine]

When I was taught this equation, we were taught how to solve it for fun, but it's quite long (I don't remember if my tutor said to memorise it or not, but my tutor told me it used ext 2 integration, so not sure). I would take a pic of my notes, but as I don't have them right now, here's the solution and how to get it: https://math.libretexts.org/Bookshelves/Calculus/Book:_Calculus_(OpenStax)/08:_Introduction_to_Differential_Equations/8.4:_The_Logistic_Equation#:~:text=dPdt=rP(1−PK,relative to the carrying capacity.

(Scroll down to 'Solving the Logistic Differential Equation')

Cool website

 

[HeeeHeee]

Thanks lads