/sci/ - Science & Math

>>5781778
>treating dy and dx as separate variables
>now you're thinking with mathematics

take d/x * d/y (cos*12)^2

>>5781811
>d/x
>d/y
wut

>>5781778
The derivative of f(y) with respect to x is df/dy * dy/dx.

>>5781778
Depends on the equation, there are various methods, not hard to learn until you get into weird pulse/step functions, and even then not bad. Take a DiffEq class or pick up a text book.

>>5781778
funny. I just wanted to tell you to fucking google it, but right now I can't even find myself a version, that doesn't argue with
>hurr and now we multiply with dx on both sides durr.
I remember doing the rigorous proof in an ode lecture, so you might find it in some lecture notes.
The only thing I found, that could help you is
http://de.wikipedia.org/wiki/Trennung_der_Ver%C3%A4nderlichen
if you know german. The english wiki doesn't do the proof

>>5781820
I am taking a diff-eq class, but due to shitty scheduling I'm taking one for engineers. That means that everything is done by splitting the dy/dx and treating them as separate variables. I don't know if this is avoided in a normal diff-eq class.

multiply it by an integrating factor

Just think about it as integrating both sides of the diff. equation w.r.t x, rather than splitting dy/dx.

>>5781822
Thank you, unfortunately I don't speak German. I have been trying various google searches but all I'm getting are people saying that splitting them is meaningless and then vague statements about the chain rule. Also people saying that you can split them.

I get the feeling that it's something obvious but for some reason it's just flying over my head. I know it's asking for a lot but could anyone please work an example (even a babby one) where you would normally split dy/dx to solve it.

<span class="math">(\cos(x)+\ln(y))dx+(\frac{x}{y}+e^{y})dy=0[/spoiler]

Here is a separable equation example, yes they give it to us written with the dx/dy split up already.

>>5781839
And what's wrong with splitting it, exactly? Thinking of it in terms of infinitesmals may not be exactly correct, but it gives a good intuitive understanding of what's happening.

>>5781835
I've been playing with this some just now, it's kind of boggling my mind. I don't feel I'm doing it right.

>>5781846
Well I'm aware that the computations all turn out correct and that it's probably fine as a shortcut, but I'm in the process of reviewing a lot of mathematical fields after a very long hiatus (over a decade) and I'd like to do it right from the get go this time. I know this is covered more in analysis which I never took before and may be good to know once I get to galois theory in algebra as I understand there's a branch of galois theory that focuses on differentials (what can and can't be solved with integral and differential).

linear algebra, look for eigenvalues and eigenvectors, its very simple, too

>>5781850
>I've been playing with this some just now, it's kind of boggling my mind. I don't feel I'm doing it right.
You could just think about it in terms of antiderivatives. If you can write your equation as f'(y)dy/dx = g'(x) then f(y) = g(x)+c. You can verify this with the chain rule by deriving both sides with respect to x.

Matrixes, only way to deal with ODEs.

>>5781862
>Matrixes

If you don't like dx, you can usually get the same results if you write it as dx/du where u is an arbitrary parameter.

>>5781846
Because you can hardly solve any equations by "splitting" it.

Here OP, this site goes through various types of differential equation. Even gets into Laplace transforms and step functions I think.

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

>>5781862
>Matrixes
Stop hurtin' me dawg

lets take f(x)/g(y) = dy/dx.

splitting it would be f(x)dx = g(y)dy
and then you integrate.
<div class="math"> \int f(x)dx = \int g(y)dy </div>
this is shorthand for:

f(x)/g(y) = dy/dx

but dy/dx = dy/dt * dt/dx
with t some function

so it becomes f(x)dx/dt = g(y)dy/dt

now integrate both sides with regards to t.

<div class="math"> \int f(x)\frac{dx}{dt}dt = \int g(y)\frac{dy}{dt}dt </div>

doing the reverse of substitution you can eliminate the dt's and get
<div class="math"> \int f(x)dx = \int g(y)dy </div>

>>5781778
Who cares?

It annoys Mathematicians treating dx and dy as variables. That's all the more reason to do it. They can stick to their mental masturbation and arguing over "proper" ways to do things. I'll use what works and spend the time developing a beautiful elegant physical theory.

>>5781778
>the proper way

No such thing.

>>5781811
The fuck is:
<span class="math">\frac{d}{x}[/spoiler] and <span class="math">\frac{d}{y}[/spoiler] ?

I think you mean,
<span class="math">dx[/spoiler] and <span class="math">dy[/spoiler]

>>5781965
"doing the reverse of substitution you can eliminate the dt's and get"

Not really the 'reverse'; the differential operators (dt) will cancel as a direct result of the FTC.

>>5782032
>FTC

I'm not that guy, but it took me a bit there to realize that meant Fundamental Theorem of Calculus. My mind went to Federal Trade Commission immediately for some reason and I couldn't think anything else.

http://en.wikipedia.org/wiki/Separation_of_variables#Alternative_notation

>>5782045
I think you meant your Google search ability took you there...

For anyone who has covered the fundamental theorem of calculus (intimately) you should know the abbreviation as intimately as you would use <span class="math">\forall [/spoiler] for "for all" and <span class="math">\angle [/spoiler] for "angle".
It's shorthand.

If you want to use the FTC as a lemma to prove something else, you don't want to write it 20,000 fucking times.

>>5781965
>and then you integrate.
"Integrating" without respect to anything, over no set, interesting.

>>5782081
>"Integrating" without respect to anything
He explicitly showed the differential next to the integrand.

What the fuck are you talking about?

>>5781871
>>5781923
I hope you aren't disputing the use of matrixes to solve ODEs but rather suggesting that I write matrices instead.
PS. Matrixes is more similar to the singular form and is just as easy to say as matrices.

>>5782113
They are implying your shit use of matrixes.

Repeat after me.

May Treh Seas.

May Trix Eh's rubs me the wrong way.

>>5782116
I'm clearly aware of the alternate form, I still prefer mine, and since there is literally no chance of confusion I'm not too bothered.

>>5782090
The differentials were already there, what the fuck are you talking about?

Nothing wrong with multiplying by dx - that's what differential forms are for.

I like Laplace for linear differential equations. No, I don't really like it, I just detest it less then the other methods.

>>5781829
>engineers
>in charge of learning mathematics

Only the most basic engineering can be done with that knowledge. It's definitely a start, but hopefully your school requires a course that teaches more methods, or you will all be scratching your heads at anything beyond simple harmonic motion.

>>5782470
I hope you're joking about that. My DE class for engineers taught how to solve that and more. A list of topics? (Not exhaustive but:) Methods for solving n-th order linear DEs with constant coefficients, first and second order DEs, Fourier series, and PDEs with applications to the wave equation, heat equation, and Laplace equation.

>>5782508
That sounds like a well-rounded DE class, similar to what I took. I was talking about the unfortunate anon whose class only did separable ODEs.
I was just poking fun at engineers, nothing more.

>>5781778
nigger there and litteraly tons of diferentials ecuations and tons of resolutions technics...
It all depends on what kind of ecuation you want to solve..

>>5781778
it's the easiest way to solve separable DEs, but when you have something different you need a different solution method...

The first few alternative routes that come to mind:
http://mathworld.wolfram.com/IntegratingFactor.html
Identities such as x(dy)+y(dx)=d(xy), produced using the chain rule (probably what you were talking about)
http://mathworld.wolfram.com/LaplaceTransform.html

>>5782550
I (like) to think any reputable engineering school would have a more elaborate DE class. My class ended with laplace transforms, but separable ODEs was like the first 2 weeks of class only

>>5782550
no I didn't mean that they did only separable ODEs, but that throughout the course they treated dy and dx as separate variables.

They also do integration by parts in some crazy way with arrows.

>>5781862

out of here you fucktard

test

>>5789447