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 equation problem

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    http://img546.imageshack.us/img546/1860/dequestion.jpg [Broken]

    3. The attempt at a solution

    My main problem is with the second part where it says find a solution to the DE that satisfies the initial condition x(π) = 2. I found the general solution to be

    [itex]x(t) = \frac{1}{9 t} \ sin \ 3t - \frac{1}{3} \ cos \ 3t + \frac{c}{t}[/itex]

    So when we substitute in we get

    [itex]x(\pi) = 2 = \frac{1}{9 \pi} \ sin \ 3 \pi - \frac{1}{3} \ cos \ 3 \pi + \frac{c}{\pi}[/itex]

    Now I need to solve for the constant C. So my question is: Do I need to calculate this using radians or degrees? I mean, should I have my calculators settings on degrees or radians? :confused:

    By the way this is how I solved the DE:

    [itex]\frac{dx}{dt} + \frac{x}{t} = sin \ 3t[/itex]

    using the integrating factor

    [itex]\mu (t) = e^{\int \frac{1}{t} dt}= k \ e^{\ln |t|} = t[/itex]

    [itex]t \frac{dx}{dt} + t \frac{x}{t}= t(sin \ 3t)[/itex]

    [itex]\int \frac{d}{dt} tx = \int t \ sin \ 3t[/itex]

    Using integration by parts for the RHS

    [itex]tx = \frac{1}{9} \ sin \ 3t - \frac{t}{3} \ cos \ 3t + k[/itex]

    [itex]\therefore \ x(t) = \frac{1}{9 t} \ sin \ 3t - \frac{1}{3} \ cos \ 3t + \frac{c}{t}[/itex]

    Is this correct? I think I solved it correctly, but I would still appreciate it if anyone could let me know if there are any mistakes. I'm a bit unsure because most of the DE solutions I've seen don't have a variable in the denominator like the 1/9t term.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 31, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi roam! :wink:

    yes, your general solution is fine :smile:
    you always use radians

    always always always! :biggrin:

    (though you shouldn't need a calculator for cos3π and sin3π :wink:)
     
  4. Mar 31, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Always use radians in calculus. The formulas become quite messy if you use degrees. For example, if we measure the angle x in degrees we have (d/dx) sin(x) = (π/180)*cos(x) and (d/dx) cos(x) = -(π/180)*sin(x).

    RGV
     
    Last edited by a moderator: May 5, 2017
  5. Apr 3, 2012 #4
    Ah I see! Thanks a lot tiny tim and Ray for your responses, I get it now!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential equation problem
Loading...