Diff EQ IVP: Non-elementary integration

- Psymon

Diff EQ IVP: Non-elementary integration

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- Psymon

\[\frac{ d ^{2}y }{ dx ^{2} }=e ^{-x ^{2}}\]
\[ y'(3) = 1, y(3) = 5 \]

- Psymon

Non-elementary integration obviously :/

- 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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## More answers

- anonymous

HELP ME WITHMY PROBLEM http://openstudy.com/study#/updates/52201a9ae4b0750826e1352a

- dan815

@Loser66

- dan815

yo are the one that did differentials like 2 days ago!!

- dan815

ive forgotten all about diff equation methods!!

- dan815

2nd order non homogenous equation so

- dan815

you could use that formula

- dan815

the variation of paremeter formula

- dan815

solve y''=0
gets your general equation and plug into variation of paremeter formula

- 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

http://www.youtube.com/watch?v=fKP-qFY-L9g

- dan815

oh i see okay

- dan815

i know then!! assume solution

- dan815

no i dont remember!!

- dan815

what are the other ways asgain?

- dan815

there undetermined coeff, cauchy way, the e^mx way, and the all working variation of parmenets and wronskin way

- 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

which method u learn till that will help

- 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

Yes it is.

- Psymon

Then ol' prof be trollin me xD

- Psymon

Yeah, this was hw given to us after the 3rd lecture, he just didnt go over it yet.

- 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

Lol, well Im trying to think of everything Ive done before that would make any sense.

- Psymon

No worries ^_^ Sorry this is such a funky question.

- Psymon

Some piece of crap one, lol. "A First Course in Differential Equations With Applications" Author zill.

- Psymon

err....Theres two, ill just put both:
!SBN-13: 978-1-111-82705-2
ISBN-10: 1-111-82705-2

- Psymon

You found it? :o

- Psymon

Can you show me where by chance?

- Psymon

Howd you get that? xD

- Psymon

You just bought it? O.o

- dan815

any progress on this yet?

- dan815

why dont you solve with power series i want to see that solution

- Psymon

Yeah. Looks like loser has a solution manual and I have an example x_x

- dan815

kk

- Psymon

Ex:
\[\frac{ dy }{ dx }=x ^{x ^{2}}; y(0) = 3\]

- Psymon

I wanted to show this before I just took the solution >.<

- 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

@SithsAndGiggles help him, please. ha!! you are lucky.

- 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

That was the example I found on it.

- Loser66

you have SithAndAngle here, I have nothing to do. hehehe.. I need sleep.

- Psymon

Lol, night then xD

- Psymon

Ooops, typo on the limits in the example obviously x_x

- Psymon

The integral parts are correct, just what I actually typed is off, I meant 0 to x, lol.

- 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

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

You're welcome

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