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learning differential equations...

C

cirthix

Diamond Member
I've got a midterm tomorrow and need to learn how to do first and second order differential equations. Does anyone know of any good websites to check out? any tips?

just as an update: i am now profecient enough in differential equations to do the sample midterm very quickly and without trouble 🙂. I understand the process, my dad helped me through the book and clarified some things. Thanks for the help guys, i appreciate it. if anything, i just had to prove you doubters wrong 😀. i'll update again tomorrow after my test. that should give me a good idea of where i stand. anyways, i'm off to do some homework and crash, goodnight all 🙂

update2: the exam went well. i had enough time to do all of it. i couldnt figure out one of them and only had a little trouble with another. i passed for sure yay 🙂
 
Originally posted by: cirthix
I've got a midterm tomorrow and need to learn how to do first and second order differential equations. Does anyone know of any good websites to check out? any tips?
Click to expand...

Don't procrastinate! 😉

 
sigh... the text book doesnt explain it very clearly and i havent been procrastinating much. i just can't seemt o make sense of them
 
ok, here's one from my sample midterm.

Give one solution of the equation y''(x) + y'(x)-2y(x) = sin(x).

Please explain each step, i know its a lot of work, but i need to understand how to do them.
 
y(x) = Acos(x) + Bsin(x)
y'(x) = -Asin(x) + Bcos(x)
y''(x) = -Acos(x) - Bsin(x)

-Acos(x) - Bsin(x) - Asin(x) + Bcos(x) - 2Acos(x) - 2Bsin(x) = sin(x)

-3A + B = 0
-3B - A = 1

B = -3/10
A = -1/10

y(x) = (-1/10)cos(x) - (3/10)sin(x)

EDIT: I think it's right now.
 
MIT has some lectures availible in RealMedia format. Check them out here.

Quick question, do you know the Laplace Transform? It can really speed up solving linear ODEs.
 
Originally posted by: cirthix
I've got a midterm tomorrow and need to learn how to do first and second order differential equations. Does anyone know of any good websites to check out? any tips?
Click to expand...

Let me see if I've got this right...

Midterm is tomorrow.
You waited until the night before to post for help.
You don't understand the material.
Differential Equations.

Quite frankly,
You're fvcked.


Of course, I could be wrong. Some people don't need to practice many problems before they really get the hang of it. Then again, those aren't the people who ask, the night before the midterm, "how do you do this stuff?"
 
we've covered differential equations for three lectures last week and i semi-understood the material. i keep getting stuck when i do practice problems so i figured i'd ask for help. its not really procrastinating when i've had the stuff for a week and have actively looked at it and worked on problems for the past couple of days.

kirckaptian, i'll be sure to watch those when i get home, thanks for the link.

randomvariable, i'm gonna look over that now, i might pm you a few questions though 😛
 
just as an update: i am now profecient enough in differential equations to do the sample midterm very quickly and without trouble 🙂. I understand the process, my dad helped me through the book and clarified some things. Thanks for the help guys, i appreciate it. if anything, i just had to prove you doubters wrong 😀. i'll update again tomorrow after my test. that should give me a good idea of where i stand. anyways, i'm off to do some homework and crash, goodnight all 🙂
 
Good luck!
When I first posted, I was thinking that it was a differential equations course.

What course is it that you're getting to first and second order diff eq's a week before the midterm?
 
Differntial equations is the bane of my existance. Fall 2004 I got a 28 (?!) in my Intro to Diff. Eqs. course (foriegn prof couldn't teach) Then in Spring 2005 I retook the course and all was going well (92 on the midterm) until the first day of exams I ended up in the operating room. Now I have to wait until April 2006 to finally rid myself of this evil creature that they call differential equations.

But good luck!
 
Good Luck with your exams.....

Personally, I hate Calculus...... I always get lowest marks in subjects which are heavily calculus-oriented......
 
the exam went well. i had enough time to do all of it. i couldnt figure out one of them and only had a little trouble with another. i passed for sure
 
Originally posted by: cirthix
the exam went well. i had enough time to do all of it. i couldnt figure out one of them and only had a little trouble with another. i passed for sure
Click to expand...

:thumbsup: 😀 :cookie:
 
Hated that stuff. Forgot 100% of it.
It never has come in useful in my life, and never will.
 
Originally posted by: Random Variable
y(x) = Acos(x) + Bsin(x)
y'(x) = -Asin(x) + Bcos(x)
y''(x) = -Acos(x) - Bsin(x)

-Acos(x) - Bsin(x) - Asin(x) + Bcos(x) - 2Acos(x) - 2Bsin(x) = sin(x)

-3A + B = 0
-3B - A = 1

B = -3/10
A = -1/10

y(x) = (-1/10)cos(x) - (3/10)sin(x)

EDIT: I think it's right now.
Click to expand...

Actually, that's only the particular solution. You also need to solve the homogenous equation:

y" + y' - 2y = 0

=> r^2 + r - 2 = 0
(r-1)(r+2) = 0
r = 1 or r = -2

Therefore, the solution to the homogenous equation is:

y_c (x) = c1*e^x + c2*e^(-2x) for constants c1 and c2.

Then, the solution to the original ODE is the superposition of the solution to the homogenous and the particular (which Random Variable found). So you end up getting:

y(x) = c1*e^x + c2*e^-2x - (1/10)cos(x) - (3/10)sin(x)

Here, c1 and c2 are constants that you can find by applying initial conditions.
 
Originally posted by: SampSon
Hated that stuff. Forgot 100% of it.
It never has come in useful in my life, and never will.
Click to expand...

I have always thought about that. What is the actual use of Calculus in practical life?

If we ever need any such things during one's job, there are always books, references, etc available. Why try to learn all these procedure and stuff?
 
holy crap...i'm failing diff eq now and that problem is rediculously easy. if that is the hardest one on your test, i would ace it so fast. seriously every one of the 10 problems on my last test was much harder than that, and i had enough time to do about half
 
Originally posted by: iwantanewcomputer
holy crap...i'm failing diff eq now and that problem is rediculously easy. if that is the hardest one on your test, i would ace it so fast. seriously every one of the 10 problems on my last test was much harder than that, and i had enough time to do about half
Click to expand...

Good for you.

Edit: Care to share some of these difficult problems you speak of?
 
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