Question

Need help finding the general solution to a differential equation!

x(x+y)y'+y(3x+y)=0

Answer 1

u have to change the variable y to ux
so y=ux

Answer 2

then y'=u'x+u
put the new variable instead y to the equation.

Answer 3

whats u'?

Answer 4

it is clear that u=y/x

Answer 5

u prime

Answer 6

derivative of u

Answer 7

oh yes for the relationship between them

Answer 8

this is a way for homogeneous diff equ

Answer 9

I just don't know how to set it up, to be honest

Answer 10

ok ill help u

Answer 11

would it just be divide x(x+y) and sub

Answer 12

no just put y as a function of u and x

Answer 13

lets show

Answer 14

x(x+ux)(u'x+u)=ux(3x+ux)

Answer 15

then omit the x and solve

Answer 16

so...(x+ux)(u'x+u)=ux(3x+ux)->>>(1+u)(u'x+u)=u(3+u)

is this right??

Answer 17

pretty good.

Answer 18

because that's what I did and got the wrong answer

Answer 19

ok let us check

Answer 20

okay

Answer 21

(1+u)u'x=3u+u2-u2-u=2u____>(1+u)u'/u=2/x

Answer 22

lnu+u=2lnx+k

Answer 23

or ln(y/x)-ln(x2)=k-y/x

Answer 24

or y/x3=Cexp(y/x)

Answer 25

or y= C.x^3.exp(y/x) that Cis a constant

Answer 26

the answer in the back of the book says: x^2(2xy+y^2)=C

Answer 27

No the answer isn't right. I checked again.

Answer 28

I guess you checked the answer in a wrong number.

Answer 29

check it out.

Answer 30

No, 100% positive. I got the same thing as you the first time I did it, which is why I was confused. But I can assure you, I am looking at the right answers.

Answer 31

im sure that the answer i gave u is right.

Answer 32

I don't know what to say because the answer in the back of the book says something different.

Answer 33

maybe it can be simplified further?

Answer 34

which book are you using?

Answer 35

oh it's writing in implicit form. *I got a strange feeling that I"ve this problem before*

Answer 36

Im using differential equations & linear algebra by Edwards and Penney

Answer 37

terrible book lol

Answer 38

dude try differential equations by bear. VERY HORRIBLE

Answer 39

well its not really up to me. I have to have it for my math class

Answer 40

but there are other ebook s online right?

Answer 41

yeah, I would normally just watch youtube vids, but I get what to do here. Im just not getting the same answer as the book

Answer 42

this is the only one that is giving me trouble

Answer 43

the book wrote it in implicit form... I don't think your answer is wrong.. just have to ummm rewrite it in a certain way

Answer 44

the thing is no matter how I write it I will still have an Ln which will lead to an exp. which is not in the answer

Answer 45

must be a conversion.. like e^(ln x) would be an x

Answer 46

the only thing I can think of is to divide both sides by the y in y= C.x^3.exp(y/x) and the ln both sides

Answer 47

but I think im just going to ask my teacher because I feel like the answer is right

Answer 48

http://www.wolframalpha.com/input/?i=+x%28x%2By%29y%27%2By%283x%2By%29%3D0

Answer 49

Thanks but I need to know how to do it. :/

Answer 50

You can register at wolframapha and get two step by step solution each day

Answer 51

http://tutorial.math.lamar.edu/Classes/DE/Substitutions.aspx

Answer 52

Here is a solution that gives the answer in the book. I am attached my scanned solution
@UsukiDoll @Thefaceless

Answer 53

@ganeshie8