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!

Okay I have a problem with using variables in differential equations

  1. Jul 7, 2012 #1
    Consider the differential equation
    where I''+I=e^it where i= sqrt (-1)



    So I don't know what to do. I do know that The second derivative of
    c*t*e^(i*t) is
    -c e^(i t) (-2 i+t)
    But I don't know what to do for a and b and I need help to get threw this problem before I take my test.


    a) Find c such that I(t)=cte^it is a solution.

    Is the equation given what the problem is differentiated? then would you just solve for c?



    b) Find the general solution and discuss what happens as t approaches infinity .

    How would you incorporate an infinity?
     
  2. jcsd
  3. Jul 7, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yep - you put that relation into the differential equation so every time you see an I you put that and every time you see I'' you put the second derivative and so on, then solve for c.
    It's not going to look obvious that it will work out before you begin - you just have to write it down and then figure it out.

    Hint: use limits.
     
    Last edited: Jul 7, 2012
  4. Jul 7, 2012 #3
    Thank you soooo much!



     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook