Psymon
  • Psymon
Diff EQ IVP: Non-elementary integration
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Psymon
  • Psymon
\[\frac{ d ^{2}y }{ dx ^{2} }=e ^{-x ^{2}}\] \[ y'(3) = 1, y(3) = 5 \]
Psymon
  • Psymon
Non-elementary integration obviously :/
Psymon
  • Psymon
Or is this one of those problems where you have to do some general solution or....something like a taylor series approximation? O.o

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anonymous
  • anonymous
dan815
  • dan815
@Loser66
dan815
  • dan815
yo are the one that did differentials like 2 days ago!!
dan815
  • dan815
ive forgotten all about diff equation methods!!
dan815
  • dan815
2nd order non homogenous equation so
dan815
  • dan815
you could use that formula
dan815
  • dan815
the variation of paremeter formula
dan815
  • dan815
solve y''=0 gets your general equation and plug into variation of paremeter formula
Psymon
  • Psymon
Yeah, problem is Im not allowed to do that, haha. I mean, there ARE methods, but in regards to where we've advanced in the class we don't have that option.
dan815
  • dan815
http://www.youtube.com/watch?v=fKP-qFY-L9g
dan815
  • dan815
oh i see okay
dan815
  • dan815
i know then!! assume solution
dan815
  • dan815
no i dont remember!!
dan815
  • dan815
what are the other ways asgain?
dan815
  • dan815
there undetermined coeff, cauchy way, the e^mx way, and the all working variation of parmenets and wronskin way
Psymon
  • Psymon
Yeah, I thought power series, too.....but then I thought that was cheating, haha. Well, this is the beginning of the semester, so we're not far at all. I mean, its all review for me until probably halfway through the semester, so we're barely into integrating factors. Problem is this is hw and he never went over this.
dan815
  • dan815
which method u learn till that will help
Psymon
  • Psymon
None, haha. I mean, this question is even in a section of the textbook where theres no crazy techniques shown. This is a chapter 2 question, haha. Thats why I was thinkin gmaybe power series because what else could we possibly know as a way to solve it when we're only in chapter 2? x_x
Psymon
  • Psymon
Yes it is.
Psymon
  • Psymon
Then ol' prof be trollin me xD
Psymon
  • Psymon
Yeah, this was hw given to us after the 3rd lecture, he just didnt go over it yet.
Psymon
  • Psymon
Ah x_x Then I think that would confirm theres some sort of old method, power series or somesort of just....general form that isnt a full solution, dunno.
Psymon
  • Psymon
Lol, well Im trying to think of everything Ive done before that would make any sense.
Psymon
  • Psymon
No worries ^_^ Sorry this is such a funky question.
Psymon
  • Psymon
Some piece of crap one, lol. "A First Course in Differential Equations With Applications" Author zill.
Psymon
  • Psymon
err....Theres two, ill just put both: !SBN-13: 978-1-111-82705-2 ISBN-10: 1-111-82705-2
Psymon
  • Psymon
You found it? :o
Psymon
  • Psymon
Can you show me where by chance?
Psymon
  • Psymon
Howd you get that? xD
Psymon
  • Psymon
You just bought it? O.o
dan815
  • dan815
any progress on this yet?
dan815
  • dan815
why dont you solve with power series i want to see that solution
Psymon
  • Psymon
Yeah. Looks like loser has a solution manual and I have an example x_x
dan815
  • dan815
kk
Psymon
  • Psymon
Ex: \[\frac{ dy }{ dx }=x ^{x ^{2}}; y(0) = 3\]
Psymon
  • Psymon
I wanted to show this before I just took the solution >.<
Loser66
  • Loser66
You know that in this level, people don 't give you step by step. They jump from this part to another part. My prof, in class, jumps as if we, students, are his Ph.D classmates. ha!!!
Loser66
  • Loser66
@SithsAndGiggles help him, please. ha!! you are lucky.
Psymon
  • Psymon
\[\int\limits_{0}^{x}\frac{ dy }{ dt }=\int\limits_{0}^{x}t ^{t ^{2}} \] y(t) limits x to 3: \[y(x) - y(0) \] \[y(x) = 3 + \int\limits_{0}^{x}t ^{t ^{2}} \] Make any sense?
Psymon
  • Psymon
That was the example I found on it.
Loser66
  • Loser66
you have SithAndAngle here, I have nothing to do. hehehe.. I need sleep.
Psymon
  • Psymon
Lol, night then xD
Psymon
  • Psymon
Ooops, typo on the limits in the example obviously x_x
Psymon
  • Psymon
The integral parts are correct, just what I actually typed is off, I meant 0 to x, lol.
anonymous
  • anonymous
For this kind of problem, I remember learning this formula: Given some initial condition \(y(x_0)=y_0\), the solution to the following DE is \[y'=f(t)~~\Rightarrow~~y=\int_{x_0}^xf(t)~dt+y_0 \] So, extending this to the second order case, you'd have \[\frac{d^2y}{dt^2}=e^{-x^2}\] \[\frac{dy}{dt}=\int_{x_0}^xe^{-x^2}~dx+y'_0\] Here, \(y'(x_0)=y'_0\), so \(x_0=3\) and \(y'_0=1\). Similarly, \[y(t)=\int_{x_0}^x\left(\int_{x_0}^xe^{-x^2}~dx+y'_0\right)~dx+y_0\] And here, \(x_0=3\) again, and \(y_0=5\), as per initial conditions.
Psymon
  • Psymon
Oh wow O.o So just kind of a general solution method. Not supposed to truly get a full answer. Yeah, Ill write that down, that's awesome! ^_^ Thanks.
anonymous
  • anonymous
You're welcome

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