Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Differential Equations help!

Announcements Posted on
    • Thread Starter
    • 1 follower
    Offline

    ReputationRep:
    Can someone give me a step by step guide of how to intergrate this?
    x(dy/dx) = 2y + 1/y
    Thanks! and any useful techniques of doing similar ones!
    • 1 follower
    Offline

    ReputationRep:
    you can start by collecting terms on the RHS, so the equation looks like:

    x(dy/dx) = (2y^2+1)/y,

    then take the reciprocal of each side, to get:

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

    multiply both sides by dy:

    (1/x)dx =[ y/(2y^2+1)]dy

    what do you notice about the RHS? - could it be like: f '(x)/ f(x) ? - you`ll need to give f ' (x) a factor of 4, while multiplying the RHS by (1/4)

    EDIT: the key point about this technique - called "seperation of variables" - is exactly that - that you are able to physically "seperate" the x`s from the y`s on either side of (or sometimes the same side) the equation (don`t forget to add the constant to the x side)

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: May 30, 2012
New on TSR

GCSE mocks revision

Talk study tips this weekend

Article updates
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.