Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

spyros

  • 2 years ago

y''=(1+y'^2)/2y

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

    \[y \prime \prime=\frac{1+y \prime ^2}{2y}\]

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

    hint : \[y\prime=u(x)\]

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

    maybe putting it like this\[y = 1+u ^{2}/2u'\]

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

    its expressed in terms of u and its drivative, so guess thats it

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

    y=y(x)

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

    we were told to substitute y' by u(x) solve for u(x) then for y(x)

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

    \[\frac{du(x)}{dx}=\frac{1+u(x)^2}{2y(x)} ,y(x)=\int\limits_{}^{}{u(x)}\]

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

    i think you need to make u a function of y u(y) = y' then y'' = u*(du/dy)

  9. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Putting \(\large u=\frac{dy}{dx}\) gives \(\large \frac{d^2y}{dx^2}=\frac{du}{dx}=\frac{dy}{dx}\frac{du}{dy}=u\frac{du}{dy}.\) Substitute that in your DE.

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

    will do

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

    rearrange it so it looks like \[\frac{2u*du}{1+u^{2}} = \frac{dy}{y}\]

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.