Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Study23

  • one year ago

Solve the differentiable equation: dy/dx = y^2 ?

  • This Question is Closed
  1. openstudy11
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2y

  2. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You mean separable, right? :D

  3. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and lol, @openstudy11 It is unfortunately not that simple :D

  4. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Study23 Shall we? :)

  5. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yup :D

  6. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay, thing about separable differential equations... they are.... separable! LOL Yeah, I know, big surprise :) What I mean is that you can rearrange them so that you can separate them into expressions involving only y and involving only x. Let's have a look at this \[\huge \frac{dy}{dx} = y^2\] You can treat the dy and dx as variables like any other, when separating. Just you try multiplying both sides by dx, and what do you get?

  7. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    dy = y^2 dx; I was doing this but I got confused because you couldn't integrate this could you?

  8. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Not yet. Now, you could bring all expressions involving y, to the appropriate side of the equation (namely, the side with the dy) You could do this by multiplying \(\large y^{-2}\) or \(\Large \frac1{y^2}\) on both sides, and what would you get then?

  9. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    dy/y^2=dx (?)

  10. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Correct :D \[\huge \frac{dy}{y^2}=dx\] Now, slip a \(\Huge \int\) sign on both sides of the equation~ and be done with it :D

  11. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, ln|y^2|=x ?

  12. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oh... \[\huge \int \frac{1}{y^2}dy \ = \int dx\] Are you sure? Maybe this ought to refresh you \[\huge \int y^{-2}dy \ = \int dx\]

  13. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay, we started with this, right \[\huge \frac{dy}{y^2}=dx\] And we simply integrated both sides \[\huge\color{blue}\int \frac{dy}{y^2}=\color{blue}{\int}dx\] And yes.... \[\huge \int ax^n=\frac{x^{n+1}}{n+1} \] when \(n\ne -1\)

  14. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Sorry, my bad \[\huge \int ax^n = \frac{ax^{n+1}}{n+1}\]

  15. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, I get \(\ \Huge -y^-1 + C_1 = x \) ?

  16. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That should be \(\ y^{-1} \)

  17. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Mother of sizes... o.O LOL \[\huge -y^{-1}+C = x\]

  18. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If you want it as a function of y, you can bring the constant to the other side \[\huge -\frac1y=x+C_0\] and then isolate \[\huge y = -\frac1{x+C_0}\]

  19. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    But on the whole, good job :)

  20. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, my textbook has this interns of Y= ...

  21. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Waaaay ahead of you ^

  22. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In terms (autocorrect)

  23. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Already done... ^

  24. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It just needs some algebraic manipulation is all.

  25. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh, haha I didn't see that! :D. Thanks for all your help @terenzreignz ! I appreciate your encouragement! By the way, any tips for the AP Calc BC exam by the way?

  26. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I don't know what exam that is... better consult someone more familiar with it :)

  27. Study23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh haha okay. Thanks!

  28. vickky
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dy/dx=y^2 dy/y^2=dx then integrate both the side -1/y=x+c

  29. 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.