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!

Finding a solution at a point

  1. Nov 4, 2006 #1
    Give the general solution of the set of equations below:


    Which I found to be:

    Here's where I'm stuck. They want me to find the solution at t=0, (x,y,z)=(2,3,-1)

    Which the professor hasn't told us how to do this.
  2. jcsd
  3. Nov 4, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I'm sure you know how to do this. If t=0, what is x(0)? There are two ways to express this... one is from the equation for x you solved for, the other is from the point you were given. Since t=0, all those nasty exponentials go away, and you have a system of three variables with constant coefficients (which is remarkably simpler than the initial set of differential equations you solved)
  4. Nov 4, 2006 #3
    ok, so what I understand from this is that I plug t=0 into all the t's of the general solutions.


    And then do I set these equal to (x,y,z)=(2,3,-1). What is the solutions form suppose to look like?
  5. Nov 4, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Let's call [tex]C_1 C_2[/tex] and [tex]C_3[/tex] A, B, and C to make it easier.

    You know
    x(0)=3A - 3B - C=2
    y(0)=6B = 3
    z(0)=2A + 8B + 3C=-1

    So you should be able to solve for A, B and C as numbers. For example, if 6B=3, B=2. Now you know 3A-6-C = 2, and 2A + 16 + 3C = -1
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Finding a solution at a point
  1. Finding a solution (Replies: 5)

  2. Find a point (Replies: 6)

  3. Find the solution? (Replies: 13)