Help solve a Differential equation

[13olt3]

a)
Solve the differential equation:
dN/dt = k(3-N)N

where N=variable and k=constant
if N=2 when t=0 and N=1 when t=1

b) Find t when N=0.5

Thanks in advance 

[fredrick]

This is a long one, ill give it a go





    --Partial fractions(dat what der called?)




Now








also








so

Finally 

can this be simplified?


Wow that took me ages hope its right

[Glockmeister]

Using Partial Fractions



























I Thinik it looks right from here... cant be arsed going further if freddie's finished it first

[/0]

can this be simplified?

From change of base,

And another identity is

so

[fredrick]

can this be simplified?

From change of base,

And another identity is

so

Yep somehow forgot bout that, cheers

[Mao]

can this be simplified?

From change of base,

And another identity is

so

that extra identity is a bit superfluous

think of it as:

so this expression itself:

[Mao]

Also, a note (a tiny trick if you like), always use the log laws to avoid , they are very messy to deal with, it is far easier to use its equivalence
and, you should seek to express everything with one log term (having two or more is often confusing and difficult to deal with)


taking from fred's step when he found C:







given when t=1, N=1





when N=0.5

[cara.mel]

Also, a note (a tiny trick if you like), always use the log laws to avoid , they are very messy to deal with, it is far easier to use its equivalence
and, you should seek to express everything with one log term (having two or more is often confusing and difficult to deal with

How did you do that?
What are Log Law?
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