Question

how do you solve this differential equation?
(y+1)dx+(4x-y)dy=0 ??

Answer 1

I was going to say split it up

(y+1)dx+(4x-y)dy=0

dx/(4x-y)=-dy/(y+1)

Answer 2

But you are still left with a y in the left side.

Answer 3

yeah xD

Answer 4

Sorry just throwing out ideas hoping you might catch something.

Answer 5

@shinigami1m you can use exact differential equation...do you know how to use that?

Answer 6

wait i mean integrating factor for exact differential equation

Answer 7

like partial M and partial N?

Answer 8

you can also use the bloody and morbid homogeneous

Answer 9

Oh is this when you take a derivative of each one plug it in to each other integrate and so on?

Answer 10

@shinigami1m this is what im talking about...it's not discussed in most schools so i dont know if you know it...

http://openstudy.com/updates/4fd16ab5e4b057e7d220ae39

Answer 11

Gj on the tutorial @lgbasallote

Answer 12

i know that method :D

Answer 13

i got (y+1)^3 for integrating factor

Answer 14

wait..why?
\[\frac{\partial M}{\partial y} - \frac{\partial N}{\partial x} = 4 - 1 = 3\]
right?

Answer 15

yes

Answer 16

wait i mean -3

Answer 17

umm its 1-4

Answer 18

it's 1- 4

Answer 19

then you divide it by M so you have \[-\frac{3}{y+1}\]
right?

btw thanks @Romero

Answer 20

yep

Answer 21

then you use \[e^{-\int g(y)dy}\] right?

Answer 22

yeeeee

Answer 23

so you have \[\huge e^{\int \frac{3}{y+1}dy}\]
agree?

Answer 24

agree

Answer 25

lol yeah it's (y+1)^3 sorry :p haha

Answer 26

HAHA the hard part is the next part... :| distributing I.F.!!

Answer 27

so i guess using homogeneous is easier in this one :/

Answer 28

its not homogenous i think

Answer 29

hmm yeah...darn y+1 -_-

Answer 30

how about linear DE?

Answer 31

it's linear in y

Answer 32

\[\frac{dx}{dy} + (\frac{4}{y+1})x = \frac{y}{y+1}\]

Answer 33

i'm at the final part... i just need to integrate -y(y+1)^3dy~~~~

Answer 34

lol this is nice...there are a lot of ways to solve this...

which method did you use?

Answer 35

exactness i just continued it haha... i think linearity is easier

Answer 36

yeah it is lol

Answer 37

IF = (y+1)^4 i think

Answer 38

that is if we use linearity haha y(y+1)^3 on the other side still XD but i got the answer hhehe

Answer 39

I always like youtubing these to see how other people do it. I like this one

http://www.youtube.com/watch?v=bwASJWS8ltM

You know I hear that you are able to retain information better if you do more study more than one way. Like reading and hearing other people then you doing it by yourself.

Answer 40

So I hope that helps.