# Differential equationWatch

#1
I've got .

I've rearranged to get .

Where do I go from here?
0
8 years ago
#2
rearrange to get y'= y/x + exp(y/x)

Then use the substitution u = y/x and see what happens
0
#3
(Original post by spex)
rearrange to get y'= y/x + exp(y/x)

Then use the substitution u = y/x and see what happens
You mean ?

Assuming I did everything correctly (integrating both sides and then subbing ), I've got . Can't see how to make the subject
0
8 years ago
#4
(Original post by Miss Mary)
You mean ?

Assuming I did everything correctly (integrating both sides and then subbing ), I've got . Can't see how to make the subject
If you're using the substitution .

You have to change so that the whole DE is in terms of u and x only. You don't want to be integrating with y's, x's and u's.
0
#5
(Original post by Clarity Incognito)
If you're using the substitution .

You have to change so that the whole DE is in terms of u and x only. You don't want to be integrating with y's, x's and u's.

So then...

What now?
0
8 years ago
#6
(Original post by Miss Mary)
....

So, differentiating

Now substitute into y'= y/x + exp(y/x), the y' as well as the y/x parts.
8 years ago
#7
(Original post by Miss Mary)

Above two lines do not lead on from each other. With the new substitution, what does y' become, it might be easier to look at it as
0
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