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

Find an explicit or implicit solutions to the differential equation, what now?

  • Thread starter mr_coffee
  • Start date
  • #1
1,629
1
Hello everyone, yet another obscure problem on web work. No examples like this in the book nor did the professor go over it so i was wondering if someone can let me know what exactly they are wanting me to do!

Find an explicit or implicit solutions to the differential equation
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/7b/3a599a5966a2ac65a84b6575a645b61.png [Broken]
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8616ca1dd6ce230911485b98a57fa31.png [Broken] = ?
What i did was divide through by dx, so i got
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/2c/f2d7bb6b17ac7be8cca5e4969f1a091.png [Broken]y' = 0;
Then
I let (x^2-4xy) = M, and N = x;
My = -4x;
Nx = 1;
Not exact.

Did i f this up or what? :cry:
 
Last edited by a moderator:

Answers and Replies

  • #2
69
0
I believe this is homogeneous, try the substitution y=ux


disregard that

This is linear, try looking at it this way [tex] (x^2-4xy)=-x\frac{dy}{dx} [/tex]
 
Last edited:
  • #3
1,629
1
hey I figured it out, i wasn't usre if this is what u were talking about. But if anyone was cur8ious this is my work:
http://img430.imageshack.us/img430/2407/lastscan1hu.jpg [Broken]

http://img229.imageshack.us/img229/1413/lastscan23ch.jpg [Broken]


:bugeye:
 
Last edited by a moderator:
  • #4
69
0
i see what you did but I just solved it by rewriting it as
[tex] \frac {dy}{dx}-4y=-x [/tex]

Then use the integrating factor
[tex] e^{-4x} [/tex]

Then multiply through to get

[tex]e^{-4x} \frac {dy}{dx}-e^{-4x}4y=-e^{-4x}x [/tex]

Now integrate both sides to get

[tex]e^{-4x}y=\frac{x}{4}e^{-4x}+\frac{1}{16}e^{-4x}+C [/tex]

multiply through by

[tex]e^{4x}[/tex]

and I came up with

[tex]y=\frac{x}{4}+\frac{1}{16}+Ce^{4x} [/tex]

Just seems like a few less steps than yours...same answer though

Do you have to use the exact solution method?
 
  • #5
1,629
1
Wow that was alot easier, this problem was under the Exact Equations problems, so yes he makes us do it this way, but really, it only evaluates the answer so I guess i wasn't forced to do it that way. Thanks!
 

Related Threads for: Find an explicit or implicit solutions to the differential equation, what now?

Replies
5
Views
805
Replies
5
Views
1K
Replies
7
Views
771
Replies
4
Views
5K
  • Last Post
Replies
5
Views
3K
Replies
4
Views
3K
Top