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Current time: August 20, 2019, 11:44 pm

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Differential equations
#1
Differential equations
So, in my university mathematics textbook, there is a series of tasks such as:
[Image: Screenshot-from-2019-06-13-10-49-32.png]
So, the variables can be separated, however, in order to solve the equation, you apparently need to solve an integral such as:
[Image: Screenshot-from-2019-06-13-10-55-36.png]
And that integral, as far as I know, can't be solved. Do you have any idea how to solve such equations?
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#2
RE: Differential equations
Any answers?
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#3
RE: Differential equations
Just feeling stupid here...

y = x e^(dy/dx)

dy/dx = dx/dx.e^(dy/dx) + x. d^2y/dx^2.e^(dy/dx)

dy/dx = ( 1 + d^2y/dx^2) . e^(dy/dx)

Getting rid of the exponential...

y = x. dy/dx / ( 1 + d^2y/dx^2 )
Is this solvable? I don't know...


Anyway, for help on solving weird integrals, you can always refer to the old Abramowitz: http://people.math.sfu.ca/~cbm/aands/abr...stegun.pdf

Alternatively, if you're really really really lazy, there's wolfram alpha.
It says that you have a version of d'Alembert's equation in your hands.
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#4
RE: Differential equations
Quote: Do you have any idea how to solve such equations?

Personally, I would hire a mathematician.  Not sure what the going rate is, but I expect you could get one for a kebab and a bottle of beer.

Boru
'A man is accepted into a church for what he believes.  He is turned out for what he knows.' - Mark Twain
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#5
RE: Differential equations
(June 13, 2019 at 4:58 am)FlatAssembler Wrote: So, in my university mathematics textbook, there is a series of tasks such as:
[Image: Screenshot-from-2019-06-13-10-49-32.png]
So, the variables can be separated, however, in order to solve the equation, you apparently need to solve an integral such as:
[Image: Screenshot-from-2019-06-13-10-55-36.png]
And that integral, as far as I know, can't be solved. Do you have any idea how to solve such equations?

Matlab, Maple, Mathematica, and Derive are some software packages that you can try out.
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#6
RE: Differential equations
(June 22, 2019 at 7:53 am)Jehanne Wrote:
(June 13, 2019 at 4:58 am)FlatAssembler Wrote: So, in my university mathematics textbook, there is a series of tasks such as:
[Image: Screenshot-from-2019-06-13-10-49-32.png]
So, the variables can be separated, however, in order to solve the equation, you apparently need to solve an integral such as:
[Image: Screenshot-from-2019-06-13-10-55-36.png]
And that integral, as far as I know, can't be solved. Do you have any idea how to solve such equations?

Matlab, Maple, Mathematica, and Derive are some software packages that you can try out.

I've tried asking Wolfram Alpha, which is, as far as I know, even more powerful than any of those things, and it doesn't give me any useful answer
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#7
RE: Differential equations
(June 22, 2019 at 11:44 am)FlatAssembler Wrote:
(June 22, 2019 at 7:53 am)Jehanne Wrote: Matlab, Maple, Mathematica, and Derive are some software packages that you can try out.

I've tried asking Wolfram Alpha, which is, as far as I know, even more powerful than any of those things, and it doesn't give me any useful answer

You may be stuck with just a numerical solution; some integrals cannot be evaluated explicitly.
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#8
RE: Differential equations
(June 13, 2019 at 4:58 am)FlatAssembler Wrote: So, in my university mathematics textbook, there is a series of tasks such as:
[Image: Screenshot-from-2019-06-13-10-49-32.png]
So, the variables can be separated, however, in order to solve the equation, you apparently need to solve an integral such as:
[Image: Screenshot-from-2019-06-13-10-55-36.png]
And that integral, as far as I know, can't be solved. Do you have any idea how to solve such equations?

Isn't that what distributes power to the axles of a vehicle?
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#9
RE: Differential equations
Jehanne Wrote:You may be stuck with just a numerical solution; some integrals cannot be evaluated explicitly.
Well, I don't think the mathematics textbook would include series of tasks that cannot be solved.
Brian37 Wrote:Isn't that what distributes power to the axles of a vehicle?
I don't know what you are talking about. You are familiar with that equation from somewhere?
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#10
RE: Differential equations
(June 27, 2019 at 6:43 am)FlatAssembler Wrote:
Jehanne Wrote:You may be stuck with just a numerical solution; some integrals cannot be evaluated explicitly.
Well, I don't think the mathematics textbook would include series of tasks that cannot be solved.

A numerical analysis text is full of such problems.
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