What a shit book

the terminology tends to be all fucked up in math books for non mathematicians

this page isn't saying much. it's just defining things. e.g. the first line is defining what a system of d first order differential equations with an initial condition is (1.1)

thats a laplace transform I believe.

Jesus, that would be awful if it's supposed to be an intro book for someone not too used to reading math.

Looks like something a physishit would write to make it seem more difficult than it actually is.

To be fair. Most ODE text books suck apparently.

It's an issue many math books have due to the ego of their authors who instead of trying to make the subject palatable and understandable elect instead to jerk off by trying to show off their mad math skills and beautiful equations.

...

I haven't read it but its format looks disgusting and unreadable.

It's not. I have my copy right in front of me and that's not chapter 1. Chapter 1 Lesson 1 is about how differential equations originate using the half life of C14 as an example.

your post got deleted and you think it's valuable enough to post it again? your opinion is trash. fuck off.

I've yet to find a decent introduction to differential equations. What helped me most was just playing around with them in Mathematica. Once you get used to the mechanics of how they work on an intuitive level, the notation is secondary and you can pick up on the ideas themselves.

I'd recommend starting out by looking at systems of first order DIFFERENCE equations (the discrete-time analogue of differential equations), which are much more intuitive in the way they operate and why you might want to study them.

Wait, what post got deleted?

fuck off

Scroll to the top of the pdf and find out who the author really is.

A post I didn't post got deleted before I posted a post which was identical to the aforementioned post.

You have a lot of explaining to do.

Oh I see the thread now. It's almost saying the same thing, but not really.

Silly user.

>you probably already know ordinary diff eqs

I learned that shit in highschool, brainlet kiddo.

I guess you're implying I am somewhere passed valley of despair because I am not wrong.

>passed
No, you're still in the valley.

thanks.

You are wrong, freshman retard. Laplace transform is nowhere on that page.

>DURRR BUT IT'S AN INTEGRAL WITH RESPECT TO A VARIABLE DENOTED BY S
Fucking moron.

Ok now Im getting pissed off. Its been quite a few years since I graduated but I still know at least some of my shit even though I never use it because its fucking useless.

When you look at the wiki page. LITERALLY THE FIRST FUCKING EQUATION THAT COMES UP IS THE 2nd FUCKING EQUATION IN THAT FAGGOT TEXT BOOK PAGE.

Now go fucking fuck yourself you god damn autistic larping douche faggot.

ok nevermind. I was wrong...

Gonna print this out and jerk off onto it. God I love owning brainlets.

should probably add this line to your screen shot for authenticity.

Not OP but as someone who took Differential Equations in their first semester of uni, I would not have been able to understand this book. I don't think my class was assigned a text but I used Zill and that was good enough for me.
Just like anything, notation is only good in moderation.

p embarrassing, bro

At least he's not doubling down like some /pol/tard refusing to accept reality.

ya...

Whatever.

So use theorem to solve dy/dx +x^2 +y = C

Here are your (you)'s

stop larping

> = C
Why the long face? You from /r9k/?

some times you gotta throw potential crap out there just to confirm you are not god.

A few weeks ago there was another thread about laplace transforms I posted in. Not sure why I failed this time.

Just solve the fucking differential equation you piece of shit.

The first sentence assumes you have basic knowledge of DEs. The book's obviously not meant to be an introduction.
That book is freely available on archive.org, so it's not hard to check that you're lying.

[math]-e^{-x}((x^2-2x+2)e^{x}-K-Ce^{x})[/math], where [math]K[/math] is a constant that may be satisfied by an initial condition.

>you're lying.
Wrong.

>proceeds to produce absolutely no evidence of not lying
k

meh, bad example.

You don't need the theorem for that one. I could solve it.

Fucking annoying cuz I used to know this shit. And I dont have access to my notes right now.

jirka.org/diffyqs/
This was the book our class used.
It was easy to read

ahhh I guess maybe you do...

I cant do this right now.

It's the first page of the book, you can download a copy of it yourself from libgen and see, what more proof do you need? Post this supposed archive link so I can laugh at how you don't know how to read

archive.org/details/TenenbaumAndPollardOrdinaryDifferentialEquations
>Chapter 1
>Basic Concepts
>How Differential Equations Originate

you set s = x^2 ubstitute then integrate both sides wrt to dy and ds. then sub back in.

I think

No, I believe you don't need any theorems. I don't know anything fancy schmancy I just slapped some methods of undetermined coefficients on there. I'd also stay away from notes the most you can and really internalize everything.
As the (un-sourced, probably) Richard Feynman quote goes: "If you can't create it, then you truly don't understand it."
I'm not the guy you think you're replying to. I simply just pointed out that you didn't provide any evidence to the guy who said you're lying. Link me the exact PDF you have and I will download it and either confirm or deny if you really want.

>"Ordinary Differential Equations" by Tenenbaum & Pollard

No
>math.brown.edu/~mgulian/morris-tenenbaum-harry-pollard-ordinary-differential-equations-copy.pdf

I slipped back to Mt. Stupid over the years.

But thanks to you fuckers I have recovered back to valley of despair.

I did some digging around and I don't know what I used but it is definitely not the method of undetermined coefficients. If it helps to find the method, I did no integrations.

Im pretty sure that theorem in OP is what you use, or at least it makes it easier.

but wtf do I know...

Bro I literally solved it though, see (). I used a system of guessing you can call it. Bring the x^2 over to the side with C and make a homogeneous solution and then a particular solution based on -x^2 plus the C. This may be method of undetermined coefficients but the examples I saw online look nothing how I do it.
I don't think it's about what you know, user. It's about what you can and are willing to learn.

thanks. I can't really see how you solved it that way, so now I am going to have to go through all my notes again because this is really bugging me.

>Bring the x^2 over to the side with C

then just integrate wrt x and you're done. no theorem required.

freagin hell.

or not...

k im done.

Also, I found the book. It is here: epubs.siam.org/doi/book/10.1137/1.9780898719222
ISBN: 978-0-89871-510-1
You got the wrong book, OP.

As a linear differential equation, it obeys superposition such that the general solution to the differential equation is the sum of its homogeneous solution and its particular solution.
Solve the homo. solution [math]y'=y[/math]
Then the particular solution you need to guess a form [math]Ax^2+Bx+D[/math] (we already have C, so I picked D) that also obeys [math]y'+y=C-x^2[/math]. Differentiate your particular solution guess and solve for the coefficients. Note that if you have a particular solution that represents your homo. solution, you need to multiply it by a single dimension of the independent variable of y at a time until it no longer represents the homo. solution.

Part of me also really wants to say that this is possible using an integrating factor. Maybe even Laplace Transforms if you're a masochist.

For Laplace Transforms attempts
inside.mines.edu/~jcollis/LAPLACE.pdf

that sounds very familiar.

but what is OPs theorem for? it seems familiar too.

Laplace transforms were brutal... that much I remember.

I think it is just establishing ground that a solvable differential equation must have some anti-derivative to it (without having anything whose derivative can satisfy the equation means the equation has no solution).
I'm not a mathematician though, so I can't be too sure this is what it's saying.

Just noticed a mistake. Should be [math]y'=-y[/math] instead of [math]y'=y[/math]. Sorry about that.

maybe Im off base.

I was thinking something along the lines of ODE version of integration by parts

Integration by parts is just a method or technique of solving an integral, and the equation given is just an integral in general. This may or may not include integration by parts, depending on the functions.

Ya, I know that much at least. Still I think OP's theorem is more practical than you're suggesting here
l

For a more thought out reply, I think it has more to do with the fundamental theorem of calculus. The text states that "it is clear that [math]y(t)[/math] then has a continuous derivative", supporting the previous claim about the differential equation needing to have this integral equation to represent it since, upon differentiating, the integral changes to the function f(t,y) and y(t) of course goes to y'(t) and the constant y naught goes to zero, which matches (1.1) .

OP here, yeah my bad, I downloaded a PDF that said it was the book but it was actually some other one. the actual book is very good
I love how you accuse me of lying as if I intentionally posted the wrong book and claimed it was another, kek. why would you lie about something you can check in 2 seconds?

>why would you lie about something you can check in 2 seconds?
People lie about stupid shit over the internet all the time, user.
Also, the Veeky Forums wiki links are usually pretty good. I personally used Zill and Paul's Online Math Notes and aced the fuck out of my class.

I don't like the font. Apart from that it's fine. Can someone explain to me, why do most maths books have shit fonts ?

how come you guys all suck the other guy's dick but not mine?

i had to bitch at someone today because they were using RK4 in a scenario where RK4 was a poor choice of numerical quadrature method. i still feel bad about it

Probably being stuck in academia for so long made them blind to what anything not-shitty looks like. Or the text was written through a free-to-use LaTeX site which didn't allow other fonts.

Yeah, but it seems that this kind of "jerking off" is the fun part when writing math books.