# Mathematics differential equations

• delsoo
In summary: You need to show some effort first. In summary, the conversation is about a problem involving hand-drawn equations and working out. The person asking for help is confused and stuck on a certain part and is asking for assistance. The person responding provides some suggestions and hints, but also reminds the asker to put in effort and not to expect a complete solution.
delsoo

## Homework Statement

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

## The Attempt at a Solution

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.

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

Simon Bridge said:
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.

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

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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.

Simon Bridge said:
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.

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

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

1 person
Simon Bridge said:
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.

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

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'##.

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

sorry what do u mean by beroullli equation?

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

http://i.imgur.com/TxlevO8.jpg... well, i stucked this part now... i can't get v=o which the bead stops

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

From the Physics Forums rules, which you agreed to when you joined:
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
So no, we won't provide the full solution to your problem.

delsoo said:
well, i stucked this part now... i can't get v=o which the bead stops
... did you follow the suggestion?

delsoo said:
sorry what do u mean by beroullli equation?
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.

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

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.

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Ray Vickson said:
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.

delsoo said:

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.

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

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 don't know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS

Last edited by a moderator:
Simon Bridge said:
... so you didn't even bother to read the link in post #13: that has a partial working.

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 don't know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS

Last edited by a moderator:
That looks like a different question.
How did you get on with this one?

Simon Bridge said:
That looks like a different question.
How did you get on with this one?

can you try to check out where's my mistake please? for the previous question, i realized my mistake finally

Well done.

## 1. What is a differential equation?

A differential equation is a mathematical equation that describes how a quantity changes over time or space. It involves a function and its derivatives, and can be used to model a wide range of physical phenomena.

## 2. What are the types of differential equations?

There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve a single independent variable, while PDEs involve multiple independent variables. SDEs incorporate randomness or uncertainty into the equation.

## 3. How are differential equations used in real-world applications?

Differential equations are used in a wide range of fields, including physics, engineering, economics, and biology. They can be used to model the behavior of systems over time, predict future outcomes, and optimize processes.

## 4. What are the techniques for solving differential equations?

There are several techniques for solving differential equations, including separation of variables, substitution, and variation of parameters. Other methods include using power series, Laplace transforms, and numerical methods such as Euler's method or Runge-Kutta methods.

## 5. What are initial and boundary conditions in differential equations?

Initial conditions are values given at the starting point of a differential equation, while boundary conditions are values given at different points along the function's domain. These conditions are used to find the particular solution to a differential equation, as the general solution will have constants that can be determined using the initial and boundary conditions.

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