1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Equations Help

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve The following Equations:
    2(y+3)dx-xydy=0

    (x2-xy+y2)dx - xydy=0 use following assumption y=vx

    xy3+ex2dy=0

    3. The attempt at a solution

    I am still a novice at diff eqs but here is what I got on the first one:
    After seperating it I ended up with
    (dx/x)=(ydy)/(2y+6) Then I get stuck with integrating the side with the Y

    For the other two I believe they can not be separated and I am not sure what to do when this is the case
     
  2. jcsd
  3. Aug 23, 2011 #2

    rock.freak667

    User Avatar
    Homework Helper

    For the right side, you can rewrite it as

    y/2(y+3) dy or ½(y+3-3)/(y+3), you can simply it even further i.e. polynomial division
     
  4. Aug 23, 2011 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    For the y-integral on the first one, you can do this:[tex]\frac{1}{2}\int \frac{y}{y+3}\,dy = \frac{1}{2}\int \frac{(y+3)-3}{y+3}\,dy = \frac{1}{2}\int \left[1-\frac{3}{y+3}\right]\,dy[/tex]or you could use the substitution u=y+3.

    On the second one, what did you get when you used the substitution y=vx?
     
  5. Aug 23, 2011 #4
    I have never used the substitution method I have no clue how to use that I looked it up earlier because someone told me that but I was unable to use the examples to work that one out
     
  6. Aug 23, 2011 #5

    Mark44

    Staff: Mentor

    I don't think you wrote this correctly - there seems to be a dx missing.
     
  7. Aug 23, 2011 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    If you differentiate y=vx with respect to x, you'll get
    [tex]\frac{dy}{dx} = v + x\frac{dv}{dx}[/tex]
    Multiplying through by dx, you end up with
    [tex]dy = v \,dx + x\, dv[/tex]
    Use this and the original substitution to eliminate y from the original equation. You should find it separates then, allowing you to solve for v, from which you can then find y.
     
  8. Aug 23, 2011 #7
    ahh you are correct it is suppose to be a dx after the xy3
     
  9. Aug 23, 2011 #8
    I tried what you said and plugged stuff back in and then I Tried separating things out and I cant seem to get it to separate out I am stuck at
    X2(1-V-V2)dx=x2v2+(x3v)dv/dx)
     
  10. Aug 24, 2011 #9

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Please show your work. It's impossible to see what went wrong without seeing what you actually did.
     
  11. Aug 24, 2011 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    For (2) you are told to let y= vx and from that dy= vdx+ xdv. Replace y and dy in the equation with those. It will reduce to a separable equation.
     
  12. Aug 24, 2011 #11

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    In that case, it's pretty straightforward to see the equation separates. Why do you think it can't be separated?
     
  13. Aug 24, 2011 #12

    Mark44

    Staff: Mentor

    Also, when the variables are separated, the integration is not very difficult.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential Equations Help
Loading...