Very simple D.E.

  • Thread starter Jameson
  • Start date
  • #1
789
4
Find a solution to the following D.E.

[tex]\frac{dy}{dx} + \frac{x}{y}=0[/tex]

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

Separate variables...

[tex]ydy = -xdx[/tex]

Integrate both sides...

[tex]\frac{y^2}{2}=-\frac{x^2}{2}[/tex]

Multiply both sides by 2, and here is where my problem arises...

[tex]y^2=-x^2[/tex]

Stuck. [itex]x^2[/itex] will always be positive, so after applying the negative, I can't take the squareroot. It has to be a simple mistake. Please give a small bit of help or a small hint. :confused:
 

Answers and Replies

  • #2
Aaargh... nearly there...

[tex]y^2=-x^2+C[/tex]

Does this ring a bell?
 
  • #3
Integral
Staff Emeritus
Science Advisor
Gold Member
7,201
56
Is there some reason you must restrict yourself to the reals? Even with the constant of integration which you need (as above) there is the possibility of a complex solution. A complete problem statement will include the boundary conditions or initial values. You have not provided a complete problem statement. Without that. your solution is complete with the addion of the constant of integration.
 

Related Threads on Very simple D.E.

Replies
1
Views
1K
Replies
10
Views
14K
  • Last Post
Replies
1
Views
968
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
1K
Replies
3
Views
946
  • Last Post
Replies
0
Views
279
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
770
Top