A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

How do I solve the following differential equation? Thanks. dy/dx=(1-x-y)/(x+y)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It should be some type of u substitution, we're working on different form of separation of variables.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This is an exact differential equation. You can write it in the form\[(x+y-1)+(x+y)\frac{dy}{dx}=0\]Identify,\[M=x+y-1\]and\[N=x+y\]Then,\[\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}(=1)\]which shows this is exact. Knowing this, you can move through with solving it.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    In this method, you're looking for a function\[\psi(x,y)=c\]where c is some constant. The proof of the method shows this function should have a form such that\[\frac{\partial \psi}{\partial x}=M\]and\[\frac{\partial \psi }{\partial y}=N\]

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay this looks good. Thank you, but I think I have to do this using I substitution.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, set u=x+y

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then du=dx and you have\[\frac{dy}{du}=\frac{1-u}{u}=\frac{1}{u}-1 \rightarrow y=\log u -u=\log (x+y) -(x+y) +c\]

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    add a constant

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes yes! that's the stuff thank you

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

  10. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.