1. Not finding help here? Sign up for a free 30min 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!

Help with IVP

  1. Jun 11, 2007 #1

    ssb

    User Avatar

    1. The problem statement, all variables and given/known data

    [tex]\frac{dy}{dt}=y\cos(t)[/tex]

    Find the solution of the DE that passes through the point (-1, -1).

    2. Relevant equations



    3. The attempt at a solution

    [tex]\frac{dy}{dt}=y\cos(t)[/tex]

    [tex]\frac{1}{y}dy=cos(t)dt[/tex]

    integrate both sides:

    [tex] ln(y) = sin(t) + C [/tex]

    Normally I would plug in -1 for y and t and solve for C but I cant take the LN of -1. When I try to isolate y first then plug in, I get the same problem with t. How can I solve this? im stuck! Is it that the ln(y) is actually ln(|y|) ??????
     
  2. jcsd
  3. Jun 11, 2007 #2

    G01

    User Avatar
    Homework Helper
    Gold Member

    You figured it out for yourself in the end:smile::

    [tex]\int\frac{dy}{y}=\ln|y|[/tex]
     
    Last edited: Jun 11, 2007
  4. Jun 11, 2007 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You could do the absolute value, since ln(-y)'=ln(y)=1/y*y'. Or you could just exponentiate your solution to get y=exp(sin(t)+C)=D*exp(sin(t)). Now you can put D negative.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Help with IVP
  1. IVP problem (Replies: 3)

  2. Help with IVP (Replies: 1)

Loading...