Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

kirbykirby

  • one year ago

x^2*y' + 3xy = 1 (Linear DE)

  • This Question is Closed
  1. kirbykirby
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I divide by x^2 to get y' + (3/x)y=1/x^2 My integration factor though gives me |x|^3

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

    I dunno what to do with this absolute value :S

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

    is it \[x ^{2}y \prime +3xy=1\]

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

    yes

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

    have you tried Cautiy Eiller..?

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

    WHat's Cautiy Eiller?

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

    basically Put the differential equation in the correct initial form Find the integrating factor Multiply everything in the differential equation by and verify that the left side becomes the product rule and write it as such. Integrate both sides, make sure you properly deal with the constant of integration. Solve for the solution y(t).

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

    (I tried seeing what wolfram alpha does, but they always do Integral (1/x) as ln x, but we are supposed to do it as ln |x|)

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

    mm no.. sorry that won't work here..

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

    I get \[|x|^3y' +\frac{3|x|^3}{x}=\frac{|x|^3}{x^2}\]

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

    after multiplying te integration factor

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

    the final step is then d/dx[x^3y]=int(x) which is simple.

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

    excuse me it is x^3y=int(x) which is to say d/dx[x^3y]=x^3/x^2

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

    But we hae absolute values no? Integral (1/x) = ln|x|

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

    this yields x^3y=x^2/2 then jus divide by x^3 to get y=1/2(x^-1)

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

    How do you know if the x is always positive?

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

    Try reading some outside resources like http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx !!! I liked this site when i was a rook!

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

    COuld it be because if we say x>0, then the drop the absolute value, but if x <0, then you put -x^3 everywhere (but since the whole equation is negative, you just "divide by -1" o_o?

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

    otherwise though this solution looks correct..any problems you see?

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

    No I was mainly concerned about the absolute value

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

    Thanks though !

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

    Ignore the absolute value.

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

    yeah.

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

    Yup

  25. 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.