Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

megannicole51

solve the differential equation. assume x,y,t>0 dy/dt=-yln(y/2). y(0)=1

  • 5 months ago
  • 5 months ago

  • This Question is Closed
  1. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    so i think im doing this right so far but I'm not really sure can someone work through the steps with me?

    • 5 months ago
  2. ddog1437
    Best Response
    You've already chosen the best response.
    Medals 0

    are you taking calculus though?

    • 5 months ago
  3. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    calc 2

    • 5 months ago
  4. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ dy }{ -ylny } = \frac{ 1 }{ 2 }dt\]

    • 5 months ago
  5. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    ill show the steps i have so far and can u tell me if im right or not?

    • 5 months ago
  6. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    ive never seen it done like that actually....my professor hasnt really done any examples so i am trying to figure it out from our book which isnt helping either

    • 5 months ago
  7. megannicole51
    Best Response
    You've already chosen the best response.
    Medals 0

    @SithsAndGiggles

    • 5 months ago
  8. myininaya
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{-1}{y \ln (\frac{y}{2})} dy= dt \]

    • 5 months ago
  9. myininaya
    Best Response
    You've already chosen the best response.
    Medals 1

    He is doing separation of variables.

    • 5 months ago
  10. myininaya
    Best Response
    You've already chosen the best response.
    Medals 1

    I think he meant to divide -yln(y/2) on both sides.

    • 5 months ago
  11. myininaya
    Best Response
    You've already chosen the best response.
    Medals 1

    and then he multiplied both sides by dt

    • 5 months ago
  12. SithsAndGiggles
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks to @myininaya for pointing out my mistake: \(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles \[\frac{dy}{dt}=-y\ln\left(\frac{y}{2}\right)\\ -\frac{1}{y\ln\left(\frac{y}{2}\right)}~dy=dt\] Integrate both sides: \[-\int\frac{1}{y\ln\left(\frac{y}{2}\right)}~dy=\int dt\] First, a substitution: \(u=\dfrac{y}{2}\), or \(2u=y\), so that \(2du=dy\): \[-\int\frac{1}{2u\ln u}~(2~du)=\int dt\\ -\int\frac{1}{u \ln u}~du=\int dt\] Got everything so far? \(\color{blue}{\text{End of Quote}}\)

    • 5 months ago
    • Attachments:

See more questions >>>

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.