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# Can somebody teach me how to do 2nd Order Differential Equations - I'm really curious Watch

1. I know how to do 1st Order DE, but have never been taught how to do 2nd ODE.

I wish they were included in the A-level (non-FM) specification.

Can somebody please write a quick brief, and then set me 3 questions to solve for practice.

Thanks.
2. unless you're very good at maths you'll need more than a quick brief. have a search around on google, there are loads of explanations out there
3. (Original post by didgeridoo12uk)
unless you're very good at maths you'll need more than a quick brief. have a search around on google, there are loads of explanations out there
I scored an A* in A-level (year 12) last year?

We don't do FM A2.

4. Asking about 2nd order ODEs is a very general topic since it can include very horrible ODEs, some of which cannot even be solved by an analytic solution and have to be approximated using numerical methods. I assume you mean second order linear ODEs? If so, these are pretty easy to do.. just look around on the internet as a poster above suggested
5. (Original post by Serano)
Asking about 2nd order ODEs is a very general topic since it can include very horrible ODEs, some of which cannot even be solved by an analytic solution and have to be approximated using numerical methods. I assume you mean second order linear ODEs? If so, these are pretty easy to do.. just look around on the internet as a poster above suggested
I have the FP2 textbook somewhere in my house - borrowed it off school, shall I just read it? How easy is it to self-teach 2nd ODE?

Bare in mind, this is just out of pure curiousity, so i'm not very likely to put a lot of effort into it, until I have more free time.
6. (Original post by SingleMuslimDotCom)
I know how to do 1st Order DE, but have never been taught how to do 2nd ODE.

I wish they were included in the A-level (non-FM) specification.

Can somebody please write a quick brief, and then set me 3 questions to solve for practice.

Thanks.
Nobody will be able to explain it to you on here. We have just finished covering them in a lot of detail in my University course and we spent 2 weeks on them. They are not that complicated but there a lot of variations and different types and it takes a while to learn how to identify and solve them all.
7. It sounds like you're competent enough to manage, so the book should be plenty for you, FP2 ones are pretty simple really, it comes down to just 2 forms if I remember rightly.

And if there's anything in it you don't quite understand, there's plenty of people always jump at the chance to help with anything on here, not like you just have to leave it. Give it a go, what have you got to lose.

As for mackem's post, in 2 weeks, you didn't do them in a lot of detail. After finishing a 5 week module almost solely around them, and knowing there's large amounts that weren't covered, if you did them in a lot of detail, then you didn't leave the lecture theatre much!
There's always lots more to learn.
8. (Original post by didgeridoo12uk)
unless you're very good at maths you'll need more than a quick brief. have a search around on google, there are loads of explanations out there
Tbh, 2nd order homogeneous ODE's (or even most non-homogeneous) seem to me, to be a lot easier to solve than a lot of 1st order ODEs, they follow a much more general rule and it's a bit more mechanical and straightforward than some of the more difficult 1st order ODEs. Things like, finding the integrating factor for a 1st order ODE can be a lot more difficult than solving 2nd orders.
9. If I remember correctly, the only thing in Further Mathematics is constant coefficient 2nd-order linear ODEs. These have a well-known general solution that can be explained in a few pages - the hardest part is finding particular integrals in the non-homogeneous cases.
10. Here's a very (very) quick briefing on 2nd-order linear homogeneous differential equations with constant coefficients.

Say you have . Then when you substitute , since and , we get:

This is only equal to zero (as is on the RHS) when (since for all x).

This quadratic is called the characteristic equation of the differential equation. Suppose it has two real roots, and . Then and satisfy the differential equation. But so do multiples of them, and they still do when you add them together, and so the general solution of the differential equation is

...for arbitrary constants A and B (analogous to constants of integration). This solution is known as the "general solution".

If then instead of the above we get .

If are complex, then we can still write it as , or we can use various identities which allow us instead to express it as , where and .

If you were then told that when and when then you could find (or ) and hence find a particular solution.

The only way to make any sense of what I've just written is to try some for yourself... reading it through probably won't do anything for you.
11. (Original post by nuodai)
Here's a very (very) quick briefing on 2nd-order linear homogeneous differential equations with constant coefficients.

Say you have . Then when you substitute , since and , we get:

This is only equal to zero (as is on the RHS) when (since for all x).

This quadratic is called the characteristic equation of the differential equation. Suppose it has two real roots, and . Then and satisfy the differential equation. But so do multiples of them, and they still do when you add them together, and so the general solution of the differential equation is

...for arbitrary constants A and B (analogous to constants of integration). This solution is known as the "general solution".

If then instead of the above we get .

If are complex, then we can still write it as , or we can use various identities which allow us instead to express it as , where and .

If you were then told that when and when then you could find (or ) and hence find a particular solution.

The only way to make any sense of what I've just written is to try some for yourself... reading it through probably won't do anything for you.
This is really fantastic mate. I couldn't quite remember 2nd Order homogenous ODEs but this brought it flooding back straight away.

Good work

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