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!

Homework Help: Differentials with linear equations

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose that y(x) is the solution to the initial problem, y'=y(1-x), y(1)=e
    find y(2)


    2. Relevant equations



    3. The attempt at a solution
    This is my initial attempt:
    [itex]\frac{dy}{dx}[/itex]=y(1-x)
    [itex]\frac{dy}{y}[/itex]=(1-x)dx

    i then integrated both side to get:
    lny=-ln(1-x)+C

    and here's the problem, if i plug in 1 to find c, ln(1-x) does not exist at that point....
     
    Last edited: Mar 26, 2012
  2. jcsd
  3. Mar 26, 2012 #2
    I tried another approach:
    y'+yx=y
    (yx)'=y

    integrated both sides:
    yx=[itex]\frac{1}{2}[/itex]([itex]y^{2}[/itex]) +C

    but with this approach i wasn't able to solve for y
     
  4. Mar 26, 2012 #3
    First of all, you integrated the right hand side incorrectly. Remember, you're just integrating a polynomial.
     
  5. Mar 26, 2012 #4
    Wait a minute, (yx)'=xy'+yx'=xy'+y, not y'+yx.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook