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#1 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-22 10:39:46
Hi, is there any analytical solution for the following problems please?
If there is any, how can I find it please?
#2 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-22 06:58:28
Hi, here's my calculations:
Also, how can I find the analytical solution for the problem please?
#3 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-22 04:21:19
Hi bobbym, I got y(0.2)=0.122826... , is it correct?
By the way, shouldn't p'=0.2y'(1-y^2)-y? The answers are slightly different this way, I got y(0.1)=0.109198 and y(0.2)=0.117486. Would you check it for me please. Thanks!
#4 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-19 12:03:14
Hi bobbym, thanks very much for that, I'll have a try myself 
#5 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-19 05:59:56
Just another question, if I'm only restricted to the formula stated earlier, is there any other way to solve the problem?
#6 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-19 05:58:23
Hi bobbym,
If you can show your way of doing the question that'd be great. I was given these questions as some exercises for the test I'll be taking on Monday, and the only formula I've been taught is the one I stated, so I don't know any other ways of solving the problem.
#7 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-18 04:33:18
I use
#8 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 22:02:27
Hi bobbym,
Do I have to solve for p(x) first? How can I solve it please?
If
, do I write it as ?#9 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 12:41:20
Yes. Those two equations in post #10 are from two other problems. There are 3 problems in total, and I need to use the modified Euler's method to find the numerical solutions:
#10 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 12:07:33
I think so. The exact words from the question are "Write down the above problem as a system of first order differential equations". I'm not quite sure what it means. I've come across problems such as
But those equations all contain the term y'', I've not come across that, so not sure what to do.
#11 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 11:46:18
Also I've ben given other equations such as
and and asked to write them in the form of first order differential equation and then use the Euler's Modified method to approximate the values at x=1.1.I have no idea how to do it. Could you give me any hints please. Thanks!
#12 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 11:39:28
Phew, so that's taylor series done. XD
Thank you very much bobbym!
So now we have to rearrange the equation into a first order differential equation. This is the part that I'm not sure about. How can I make it a 1st order DE if it contains the term y''? 
#13 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 10:33:54
Oh sorry, I think I've typed it wrong, the equation should be
.Rearrange the equation I get .
#14 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 07:56:39
Um.... sorry, can't figure out what's wrong , is it that y''=/=-0.0802?
#15 Re: Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-17 02:31:05
Hi bobbym, thanks for your reply, this is the full question:
given
i) You are asked to find the approximate solution for this problem using the Taylor series method. Your expansion should include the first three non-zero terms and you should work to six decimal places accuracy. First find the approximate solutions for both y (0.1) and y(0.1) using the first three non-zero terms of Taylor series expansion for each function and then use this information to calculate the approximate solution at x = 0.2.
ii) Write down the above problem as a system of first order differential equations. Calculate the numerical solution at x = 0.2 using the Modified Euler method. Take the step-length h = 0.1 and work to 6 decimal places accuracy. Compare with your solution in part (i) and comment on your answers.
My taylor expansion is:
#16 Help Me ! » Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation. » 2012-04-16 23:25:58
- bubokribuck
- Replies: 32
First I'm asked to expand the equation into a Taylor series and obtain the approximate solution for x=0.1 and x=0.2, and the answers I've calculated are: y(0.1)=0.109599 and y(0.2)=0.118396.
Next, I'm asked to write down the above problem as a system of first order differential equations and calculate the numerical solution at x = 0.2 using the Modified Euler method. Take the step-length h = 0.1 and work to 6 decimal places accuracy.
How can I rewrite the above equation as a first order DE? Is it
?#17 Re: Help Me ! » I don't understand the question! » 2011-12-27 06:42:45
Hi bubokribuck;
It sure does and it makes the problem harder to do by the generating function approach.
I am still working on it.
Thanks, I'm working on it too. It looks like an endless nightmare 
#18 Re: Help Me ! » I don't understand the question! » 2011-12-27 05:35:00
Hi bubokribuck;
Are you making any progress yet? Here is a little hint that will allow you to handle it in a totally mechanical way.
Hi Bob, thanks for your reply. I'm still working on it, but looks like I've done it wrong again. I've asked my tutor and he said that we don't need to take the repetition into account. So does that affect the answer?
#19 Re: Help Me ! » I don't understand the question! » 2011-12-26 02:01:06
hi bubokribuck
I do not know if the following will be helpful but here goes:
You have obviously got to
Now write this as
Now treat b + c as a single number.
It can only have values from 3 (= 1 + 2) up to 17 (= 8 + 9) so will contribute part totals of 33, 44, 55 ... 187.
b and c cannot take the same values during this analysis which makes life easier.
Similarly, 10a + d can only have values from 12 to 98, giving part totals of 24, ... 196.
You will have to remove the cases where a = d from this.
And then, the hard bit I think. Remove the cases where a or d has a value already used by b or c.
It looks like it will be easier to consider the 'repeats allowed' problem first.
Hope that helps.
Bob
Hi Bob, since your suggestion, I've come up with quite a lot attempts but every time failed to reach a correct conclusion. The following is what I think I've done right so far.
#20 Re: Help Me ! » I don't understand the question! » 2011-12-17 07:16:08
Hi;
What was the method that you have been using for problems of this type?
I didn't learn any method for solving such problem. Our lecturer set it as our coursework and asked us to do our own research.
Basically I set the square as
a b
c d
So if S=200, 200-20a-2d=11(b+c) where 200-20a-2d is divisible by 11. I listed all the possible values for a and d, once all listed, I moved on to find the values for b and c.
This is the solution I've come up with for part (A) of the question, which is why I think doesn't apply to (B) as then I need to do the method for 274 times which sounds really scary
#21 Re: Help Me ! » I don't understand the question! » 2011-12-17 06:53:02
Yes, it does so you will have to go from 83 to 357.
What kind of class is this?
I'm doing a maths degree in uni
Thanks for the help!
#22 Re: Help Me ! » I don't understand the question! » 2011-12-17 06:16:15
Hi;
From 44 to 396.
But the questions says "distinct digits" though. 
But either case, does that mean I need to apply the method I used in (A) but this time for 83≤S≤357 (or 44≤S≤396)? It looks horribly time consuming, and our lecturer said that "Dont attempt to answer these questions by trial and error it will take you a very long time!".....
Would you give me a hint about how to make a start please, as I'm really confusing at the moment.
Thanks!
#23 Re: Help Me ! » I don't understand the question! » 2011-12-17 06:08:10
They want you with digits repeated or not to find all the squares that can not be constructed. If your method was good for the other S = 200 then it should apply here. Or I can run them off.
For instance even using repetitive digits 47 can not be made with that square.
So I need to set S to all the numbers range from 83 all the way to 357 and solve respectively!? 
#24 Re: Help Me ! » I don't understand the question! » 2011-12-17 05:52:52
Hi;
Okay, but there are 22 solutions for S = 200 so be careful. They did say they want all the arrangements.
Yes I got 22 for part(A), thanks.
But I'm stuck at (B) at the moment , any help please?
#25 Re: Help Me ! » I don't understand the question! » 2011-12-17 04:58:36
Hi;
Did you get all the solutions?
Do you mean if I got the values for S where a square cannot be constructed? If so, then no I didn't get the solutions.
I was just given the question as it is, and was asked to solve it on my own, but I'm a bit confused with the question itself, therefore I posted here for help