Question

Help with a diff eq. So far we have only learned how to deal with seperable DE's and first order linear DE's by using the integrating factor. I was curious if the following problem can be solved using the above methods.
(x+2)dx-(2x+y-4)dy=0
If not, how do I solve it?

Answer 1

Hmmm, sometimes you can 'distribute' differntials, then collect like terms in a way. Not sure if that's generally valid, though.

Answer 2

Lol, I thought it about it but I have never done that in my life.

Answer 3

Yeah, most mathematician types find it kinda shady, but I did it in physics all the time.

Answer 4

I know that if you just had (x+2)dx, you could integrate it as x dx + 2 dx . . .

Answer 5

I haven't done diff.eq. since 2001, '02... I'm a little rusty.

Answer 6

Well seeing has how this is a bonus problem I don't think it is that easy lol

Answer 7

I guess I could always write it down so my prof can have a laugh if it happens to not be correct

Answer 8

@lgbasallote (done any of this recently? My brain can't recall this stuff right now)

Answer 9

You can try looking up similar examples here: http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Answer 10

yes you can use linear DE here

Answer 11

...or maybe not

Answer 12

I'm wondering if it's this type here: http://tutorial.math.lamar.edu/Classes/DE/Exact.aspx

Answer 13

although...you can make this into an exact DE using integrating factors....are you familiar with that?

Answer 14

Yea I was looking at that Cliff.. We have not learned about Exact DE's yet

Answer 15

ohh...well i think that's the only way....

Answer 16

Alright Ill try and look at Pauls notes and see if i can figure it out

Answer 17

Reminds me that I need to go back and brush up on my diff.eq. I'm using Paul's Notes now to teach myself linear algebra, so maybe when I 'm done with that.
(as I keep trying to cram more stuff into this brain, other stuff keeps falling out!)

Answer 18

Khan academy and the MIT lectures is what I used for linear algebra.. Hated it at first but grew to love it lol

Answer 19

I don't really use Khan Academy for much. I love the MIT lectures. Walter Lewin for physics is the best! Isn't it Prof. Strang that does the linear algebra ones? I've tried sitting through those, but haven't made it far yet.

Answer 20

Just out of curiousity.. is how I went about solving the problem correct so far? If so this is not an exact DE either...
\[(y+2)dx-(2x+y-4)dy=0\]
Dividing through by dx
\[(y+2)-(2x+y-4)\frac{ dy }{ dx }=0\]
M= y+2
N=2x+y-4
Taking partials of M and N
\[M_{y}=1\]
\[N_{x}=2\]
\[M_{y } \neq N_{x}\]

Therefore the DE is not exact? Did I make a mistake somewhere?

Answer 21

Yes Strang is who does the Linear Alg lectures. I found them very helpful.

Answer 22

Figured it out.