# Mathematics differential equations

1. Mar 23, 2014

### delsoo

1. The problem statement, all variables and given/known data
hi, all… can anyone help me with this question? i got stucked here? can you figure out which part contains mistake or post the full solution here? thanks in advance!

http://i.imgur.com/RZpquyd.jpg?1

http://imgur.com/RZpquyd&Eoaa0mm#0

2. Relevant equations

3. The attempt at a solution

2. Mar 23, 2014

### Simon Bridge

Both pics are a bunch of hand-drawn equations and working out.
They are meaningless without the problem they belong to and the reasoning behind them, so I'll have to make some guesses in order to start helping you. In future, please try to describe the problem.

I can see a possible confusion in the line: $$k=\frac{1}{2k}\ln 3$$ ... have you used the same variable for two things here?

There is a red note: $$\frac{dy}{dx}+Py=a$$ ... if you didn't write that, then it may be a hint as to where you went wrong and you should look more closely at the DE you are trying to solve.
(I can't tell if that's supposed to be Py or Py)

$$-v\frac{dv}{dk}=h+kv^2$$ ... is what you ended up with.
Assuming that is correct, it tidies up to:$$\frac{dv}{dk}+kv=-\frac{h}{v}$$
Which has form:$$\frac{dv}{dk}+p(k)v=q(v(k))$$... which you appear to have tried to solve via an integrating factor.

I'm guessing that this is what you want help with?

If so then: Compare with "Bernoulli's Equation".
If the writing in red is a hint, it appears to suggest that the initial DE is wrong... so the mistake is off the top of the page.

Last edited: Mar 23, 2014
3. Mar 23, 2014

### delsoo

ps i add in the red note myself .... i am not sure whether can use the 'RED' method or not

4. Mar 23, 2014

### delsoo

ps i add in the red note myself .... i am not sure whether can use the 'RED' method or not

so is my working correct? here's the question by the way
http://i.imgur.com/DKtjee4.jpg?1

Last edited: Mar 23, 2014
5. Mar 23, 2014

### Simon Bridge

OK - in general - do not use red pen on your own work.

If you have a DE of form $y'+Py = Q$ where P and Q are functions of x alone, then you can go right to an integrating factor.

But you don't have that form.

You have form: $yy'+xy^2=c$: for c a given constant.

Look up how to solve Bernoulli's equation.

6. Mar 23, 2014

### delsoo

thanks for your reply! , i am still confused? would you mind to you show the full working here?

7. Mar 23, 2014

### Simon Bridge

First: Look up how to solve Bernoulli's equation.

8. Mar 23, 2014

### LCKurtz

I haven't read the images and don't plan to, but if your problem is to solve something like $yy'+xy^2 = c$, just try substituting $u= y^2,~u'=2yy'$.

9. Mar 23, 2014

### delsoo

sorry what do u mean by beroullli equation?

10. Mar 23, 2014

### delsoo

11. Mar 23, 2014

### delsoo

http://i.imgur.com/TxlevO8.jpg.... well, i stucked this part now... i cant get v=o which the bead stops

12. Mar 24, 2014

### Staff: Mentor

From the Physics Forums rules, which you agreed to when you joined:
So no, we won't provide the full solution to your problem.

13. Mar 24, 2014

### Simon Bridge

... did you follow the suggestion?

http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx

You have a relation of form: yy'+xy^2 = c (y=v, x=k, c=-h, right?)

You need to put it in form: y'+py=qyn
... hint: substitute y=1/u and solve for u.

14. Mar 24, 2014

### Ray Vickson

o
Why are you asking a question? You are asking if you are still confused. If you are confused, just say so, but do not ask whether or not you are---that is what happens when you use a question mark. Now is a good time for you to break a bad habit.

Also: PF rules state specifically that we are not allowed to show you full workings.

Last edited: Mar 24, 2014
15. Mar 24, 2014

### delsoo

16. Mar 24, 2014

### Ray Vickson

Several people have already given you several useful suggestions, but it seems that you are not willing to follow these up. It is up to YOU to do the work; that is the only way you will learn anything.

17. Mar 25, 2014

### Simon Bridge

... so you didn't even bother to read the link in post #13: that has a partial working.

18. Mar 27, 2014

### delsoo

can you take a look at this question? part b (question 1 ) , my ans is -3/2 ... but the ans given is 2/3... i dont know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS [Broken]

Last edited by a moderator: May 6, 2017
19. Mar 27, 2014

### delsoo

can you take a look at this question? part b (question 1 ) , my ans is -3/2 ... but the ans given is 2/3... i dont know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS [Broken]