• Support PF! Buy your school textbooks, materials and every day products Here!

Homogeneous DE simplification

  • Thread starter snowJT
  • Start date
118
0
This is a basic simplification, but I'm going to post this here because it becomes homogeneous, and I know [tex]v = \frac{y}{x}[/tex] but I don't see this simplification, I don't understand how it gets from this...

[tex]\frac{dy}{dx} = \frac{y-x}{y+x}[/tex]

To THIS:

[tex] = \frac{v-1}{v+1}[/tex] (I'm just only showing the RHS here)

If someone wouldn't mind explaining it, that would be great because I'm lost, unless this is a special rule.
 

Answers and Replies

cristo
Staff Emeritus
Science Advisor
8,056
72
Well, let y=vx, then sub into the RHS and you get [tex]\frac{vx-x}{vx+x}=\frac{x(v-1)}{x(v+1)}=\frac{v-1}{v+1}[/tex]
 
118
0
oh wow, that's incredible, I get it, thanks cristo
 
cristo
Staff Emeritus
Science Advisor
8,056
72
oh wow, that's incredible, I get it, thanks cristo
You're welcome!
 

Related Threads for: Homogeneous DE simplification

  • Last Post
Replies
3
Views
511
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
14
Views
2K
  • Last Post
Replies
7
Views
1K
Replies
0
Views
1K
Top