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

gerryliyana Group Title

Solve dy/dx = (x + 4y -1)^2

  • 2 years ago
  • 2 years ago

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

    solve \(\frac{ dy }{ dx } = (x + 4y -1)^{2}\)

    • 2 years ago
  2. carson889 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It is 2x + 8y - 2.

    • 2 years ago
  3. carson889 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Got it by expanding the brackets: x^2 + 4yx - x + 4xy + 16y^2 -4y -x - 4y + 1. Which simplifies to: x^2 + 8xy + 16y^2 - 2x -8y + 1. Taking the derivative of that with respect to x: 2x + 8y + 0 - 2 - 0 + 0 Which simplifies to 2x + 8y -2 or 2(x+4y-1)

    • 2 years ago
  4. carson889 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Or using chain rule: \[2(x+4y-1)^{1}(\frac{ d }{ dx }(x+4y-1))\] \[\frac{ d }{ dx } = 1\] Therfore, \[2(x+4y-1)(1) = 2x + 8y - 2\]

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

    2(x+4y-1)=2x+8y-2.

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

    ok thank all a lots i appreciate it :)

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

    No Problem.

    • 2 years ago
  8. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @carson889: wait i mean \[\frac{ dy }{ dx } = (x+4y - 1)^{}\] \((x+4y -1)^{2}\) is the result of \(\frac{ dy }{ dx }\) it isn't \[\frac{ d }{ dx} (x +4y -1)^{2}\] any idea???

    • 2 years ago
  9. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You need to use the chain rule, as this is implicit differentiation, not partial.

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

    what did u get it??

    • 2 years ago
  11. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So, are we trying to find \(y\) ?

    • 2 years ago
  12. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    (As a function of \(x\) )

    • 2 years ago
  13. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it seems like http://openstudy.com/study#/updates/50a9b0e8e4b064039cbd16a2

    • 2 years ago
  14. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, so it's an actually differential equation which you have to solve. Here:

    • 2 years ago
  15. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Define (all in terms of x): \[ v=4y+x\implies v'=4y'+1 \]So: \[ \frac{v'-1}{4}=(v-1)^2\implies\\ \frac{v'}{4v^2-8v+5}=1 \]Integrating both sides: \[ \int \frac{v'}{4v^2-8v+5}\;dx=\int 1\;dx=\\ \frac{\tan^{-1}(2v-2)}{2}=x+C \]Solving for \(v\): \[ v=\frac{\tan(2(x+C))+2}{2} \]Substituting \(y\): \[ y=\frac{\tan(2(x+C))-2x+2}{8} \] That took forever.

    • 2 years ago
  16. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome..., thank u @LolWolf

    • 2 years ago
  17. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure thing

    • 2 years ago
  18. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @LolWolf

    • 2 years ago
  19. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i tried to calculate on Maple 13, but, look at the picture below

    • 2 years ago
    1 Attachment
  20. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    is not equal to (x+4y-1)^2

    • 2 years ago
  21. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    This is the equation I get, when solving the differential with Mathematica:

    • 2 years ago
  22. LolWolf Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    In real form:

    • 2 years ago
  23. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok...,

    • 2 years ago
    1 Attachment
  24. gerryliyana Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it is right, isn't it?

    • 2 years 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.