Solving a partial differential equation

A

AntoineCure

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Hello everyone,

I don't have the mathematical skills so I'm posting here, I would like to know the solutions of this partial differential equation :
1621958960796.png
Where a is a real positive constant.

I know that there are an infinite number of solutions but I would like to know if there is a solution that satisfies to the following conditions :
1621959072113.png
b and c are also real and positive constants.

Thank you very much !
 
I think most folks would be tempted to study up and fulfill prerequisites, rather than jumping into the deep end.
 
AntoineCure said:
Hello everyone,

I don't have the mathematical skills so I'm posting here, I would like to know the solutions of this partial differential equation :
View attachment 27466
Where a is a real positive constant.

I know that there are an infinite number of solutions but I would like to know if there is a solution that satisfies to the following conditions :
View attachment 27468
b and c are also real and positive constants.

Thank you very much !
Click to expand...
What methods of solution of PDE have been taught in your course?

For the given PDE, is it a linear PDE? is it quasi-linear PDE? is it fully non-linear PDE? Why do you think so?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Hello,

Actually I am more of a chemist so I wouldn't really know how to solve that equation I have only basic notions in differential equations. I just stumbled upon this equation when I was working on something so I wanted to know if it had solutions that satisfied my conditions. But if this question is too vague or too much to ask I will remove it no problem :)
 
AntoineCure said:
Hello,

Actually I am more of a chemist so I wouldn't really know how to solve that equation I have only basic notions in differential equations. I just stumbled upon this equation when I was working on something so I wanted to know if it had solutions that satisfied my conditions. But if this question is too vague or too much to ask I will remove it no problem :)
Click to expand...
This the "problem" that you have posed. We would only help you to solve it - however solution would be yours. Now if you do not have the time nor the inclination to solve it ........

;);)
 
Subhotosh, I do not think this is a student of mathematics at all.
 
No not at all I study chemistry but I love math so much, I just don't have the skills to solve the problem I have submitted here haha. But I guess I'll just delete it
 
AntoineCure said:
I'm not sure to understand what you mean, did I ask too much ?
Click to expand...
It is a simple thing. If you REALLY have no background at all in this sort of thing, what good would a solution do you? It is VERY UNLIKEALY you would understand it.

I know nothing of chemistry, metalurgy, or electrolysis. I may have taken Organic Chemistry in college. I couldn't tell anodized aluminum from pitch blend. Should I heat the HCl before I apply the electricity or after? Would you trust me with that answer? Will you take on the liability for my errors and victims after giving me that answer?

Are your equations useful for making bombs or ICBM propulsion?

As is ALWAYS the case, we should absolutely NOT ask only CAN we do something. We should also ask SHOULD we do something. Very, VERY different questions. Both important and relevant.
 
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Actually I have a good background in mathematics I would easily understand everything you write and explain, it is just that we barely went over the partial differential equation so I don't know the methods to solve them properly but I would totally understand I think. Only at the moment I don't have time to learn how to do it and then apply it so I asked for help just in case someone would find a solution.
Actually yes this equation would be linked to chemical reactions but I don't know how to solve it because I kind of invented it
 
Hypotheticals.

AntoineCure said:
Actually I have a good background in mathematics I would easily understand everything you write and explain, it is just that we barely went over the partial differential equation so I don't know the methods to solve them properly but I would totally understand I think. Only at the moment I don't have time to learn how to do it and then apply it so I asked for help just in case someone would find a solution.
Actually yes this equation would be linked to chemical reactions but I don't know how to solve it because I kind of invented it
Click to expand...
Go read your original post, again, and point out all this useful information.

Well, someone (a few years ago) invented solutions to some PDEs. Why not do the same, yourself? Sounds like you might be up tp it.

Start Here?: Differential Equations - Partial Differential Equations (lamar.edu) I found it well-written and comprehensible, but there may be a chapter missing.
 
AntoineCure said:
Actually I have a good background in mathematics I would easily understand everything you write and explain, it is just that we barely went over the partial differential equation so I don't know the methods to solve them properly but I would totally understand I think. Only at the moment I don't have time to learn how to do it and then apply it so I asked for help just in case someone would find a solution.
Actually yes this equation would be linked to chemical reactions but I don't know how to solve it because I kind of invented it
Click to expand...
To begin the solution you must first answer the question I posed in response #4:
Subhotosh Khan said:
For the given PDE, is it a linear PDE? is it quasi-linear PDE? is it fully non-linear PDE? Why do you think so?
Click to expand...
You could begin there and we can start discussion. Next you have to answer:

The EXISTENCE and UNIQUENESS of possible solution.

Are you familiar with solution of Boundary-value problems in the domain of Ordinary Differential Equations?
 
Two dimensional, first order, nonlinear, homogeneous differential equation.

If we ignore the side conditions,

[MATH]f(x,y) = c[/MATH], is a beautiful solution

where [MATH]c[/MATH] is any real number

Another beautiful solution is

[MATH]f(x,y) = \frac{y}{1+ ax}[/MATH]
? :devilish:
 
nasi112 said:
Two dimensional, first order, nonlinear, homogeneous differential equation.

If we ignore the side conditions,

[MATH]f(x,y) = c[/MATH], is a beautiful solution

where [MATH]c[/MATH] is any real number

Another beautiful solution is

[MATH]f(x,y) = \frac{y}{1+ ax}[/MATH]
? :devilish:
Click to expand...
Those are NOT solution/s because those do not satisfy the boundary condition.

1622145183354.png
 
I know nothing about differential equations but are the first three conditions:
1622150323710.png
not incompatible with the final statement below?

[MATH]\hspace4ex \text{b and c are also real and positive constants.}[/MATH]
 
nasi112 said:
Two dimensional, first order, nonlinear, homogeneous differential equation.

If we ignore the side conditions,

[MATH]f(x,y) = c[/MATH], is a beautiful solution

where [MATH]c[/MATH] is any real number

Another beautiful solution is

[MATH]f(x,y) = \frac{y}{1+ ax}[/MATH]
? :devilish:
Click to expand...
 

You cannot call the OUTPUT of a DE a SOLUTION - if the out has NO CHANCE of satisfying the boundary condition/s.
 
Subhotosh Khan said:
You cannot call the OUTPUT of a DE a SOLUTION - if the out has NO CHANCE of satisfying the boundary condition/s.
Click to expand...
I could and I have already done it. I was not giving the solution that the OP was asking for. I have given two solutions without any restrictions.

Can you think of a third solution? (Ignore the given conditions)

One more thing, the OP has made up the conditions. It is more likely that there is no solution with the given conditions. If you can find a solution with his conditions, show us your thoughts.
 
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