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Having problems understanding differential equations

Hi there (Bow),

I'm looking for a worked example of the below question. Or for someone to walk me through what to do and what is going on please.

Attachment 30050

I can't seem to find anything online that helps me and I don't seem to have much on the topic in my books.

I've got a fair few to work through but just need to see one in action as I don't know what I'm doing (Headbang).

Thanks

Re: Having problems understanding differential equations

What exactly do you want to know? The first thing the problem says is "in the absence of species Y (i.e. y= 0)" so the two equations become

and 0= 0. (The right side of the second equation is 0 because it is 0 times something. The left hand is 0 because y is a **constant**, 0, and the derivative of a constant function is 0.)

That equation is a "separable first order equation" which is typically the first thing you study in differential equations. You can "separate" it as

Integrate on the left using "partial fractions".

Re: Having problems understanding differential equations

Re: Having problems understanding differential equations

Quote:

Originally Posted by

**jezb5**

that looks correct but you should finish by solving for x to get x = f(t,c).

Then you can use x_{0} = f(0,c) to solve for c for each of your two initial conditions.

Re: Having problems understanding differential equations

Quote:

Originally Posted by

**romsek** that looks correct but you should finish by solving for x to get x = f(t,c).

Then you can use x_{0} = f(0,c) to solve for c for each of your two initial conditions.

Thanks :)

I'm not sure how to do this bit as I don't fully understand the notation used. Could you talk me through it please?

Re: Having problems understanding differential equations

Quote:

Originally Posted by

**jezb5** Thanks :)

I'm not sure how to do this bit as I don't fully understand the notation used. Could you talk me through it please?

were you able to solve for x?

Re: Having problems understanding differential equations

Re: Having problems understanding differential equations

Re: Having problems understanding differential equations

Quote:

Originally Posted by

**romsek** While what you've done is correct it's not exactly right. You want to solve for x as a function of c and t.

You have

In the first case

just repeat this for

Thanks :)

I've nearly got this finished as a worked example.

When looking at the results for the below

Does this mean the population is growing?

and

So the population is declining?

Re: Having problems understanding differential equations

Quote:

Originally Posted by

**jezb5** Thanks :)

I've nearly got this finished as a worked example.

When looking at the results for the below

Does this mean the population is growing?

and

So the population is declining?

that's basically correct though you really need to look at the whole function. In this case though it does turn out that negative C corresponds to a decline in population while positive C corresponds to growth in population.

To see if you really understand what's going on see if you can determine what the population stabilizes at for any choice of C other than 0.