Substitution Differential Equation

  • Thread starter KillerZ
  • Start date
  • #1
116
0

Homework Statement



Solve the given initial value problem.

Homework Equations



[tex]ydx + x(lnx - lny - 1)dy = 0[/tex]

The Attempt at a Solution



I am confused as to what to do as I can't just substitute y=ux or x=vy because they are not homogeneous of the same degree. And I can't use exact because:

[tex]\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}[/tex]
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
I don't think u=x/y is such a bad start. ln(x)-ln(y)=ln(x/y)=ln(u). I haven't tried to follow it out. But I would definitely start with that.
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
Are you sure it isn't homogeneous? Remember ln(x) - ln(y) = ln(x/y)
 
  • #4
116
0
I got it thanks for the help.
 

Related Threads on Substitution Differential Equation

  • Last Post
Replies
4
Views
807
  • Last Post
Replies
1
Views
797
  • Last Post
Replies
3
Views
1K
Replies
8
Views
2K
Replies
2
Views
4K
Replies
1
Views
714
Replies
13
Views
989
Replies
2
Views
11K
Replies
2
Views
10K
Replies
4
Views
10K
Top