Question

dy/dx = (y/x) + (x/y)

Answer 1

there are 2 ways.
Do you know the integrating factor thing ?

Answer 2

Actually there are more than 2 ways, but lets stick to 2.

Answer 3

integrating factor ? i might know it, because all I did before this is without knowing their name -_-"

Answer 4

okay :D

Answer 5

Something like this :

dy/dx + p(x)y = Q

Here you multiply both sides by e^m where m= integral p(x)dx.

Does this help your case?

Answer 6

ohhhh

Answer 7

I learnt it in high school, but completely forget bout it ... i mean, i never think of using it here ._.

Answer 8

Well if you are not comfortable with this, there is another simple but lengthier method.

Answer 9

i'll try to do it, at least, im not as clueless like i were just now :D

Answer 10

ohh, what is it ? D:

Answer 11

substitute y/x = t

If you recall something? (homogeneous form)

Answer 12

that's the topic for this week, haven't learn yet ._.

Answer 13

but somehow, i did some revision beforehand, and quite understand, but I can't move it to either side to be integrated ._.

Answer 14

or maybe it just my concept is wrong.

Answer 15

Well you try it, I gtg, I'll be back in 15-20 mins.

Answer 16

okay, thanks :D

Answer 17

oh yea, i did z=x/y but, having tough time on differentiate 1/y in term of x, err, i used to differentiate xy, not x/y ._.

Answer 18

go for z=y/x and not x/y.

Answer 19

oh, it make any difference ?

Answer 20

okay, i see it :D

Answer 21

Also, integrating factor thing will not work here, I recall that Q should only be a function of x which is not our case.
So, the method we are using at the moment is the right one.

Answer 22

yea, i did it just now, n stuck halfway @.@

Answer 23

:|

Answer 24

hahaha, but still, z=y/x is a brilliant solution :D

Answer 25

So its over? you got it?

Answer 26

I meant is it over? you got the solution?

Answer 27

erm, currently doing it

Answer 28

wondering why I still stuck here -_-

Answer 29

Whats the progress?

Answer 30

still differentiating z=y/x, i thought it would be easy, guess going ahead than class is difficult afterall ...

Answer 31

z=y/x
y =zx
dy/dx = dz/dx + z

make that substitution in your original expression.

Answer 32

this is what i got ... ._.

Answer 33

wait, really ?

Answer 34

what the ... I completely differentiate the whole stuff, and turn like this
dz/dx = -y/x^2 + dy/xdx

Answer 35

and, u made it far way easier ._.

Answer 36

our purpose of substituion was to eliminate y.

Answer 37

oh, oh oh, then we simply subtitute it right ?

Answer 38

yep,

Answer 39

dang, i can't believe i spent too much time here -_-

Answer 40

seems like i was trolled by this question, btw, thanks for helping, this helping a lot in my progression :D

Answer 41

next class is going to be awesome, thanks to you :3

Answer 42

hmm
well glad I could help.