Page 2 of 2 FirstFirst 12
Results 16 to 22 of 22

Math Help - System of first order ODE

  1. #16
    Junior Member
    Joined
    Oct 2010
    Posts
    33
    I should state all linear subspaces for which the solutions for t->inf or t->-inf converge against x=0.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I think I have an idea what you mean. Let's take t\to\infty. Now, we don't know the signs of a and b, so we'll have to do different cases depending on which one we have. We may be able to do something clever with the signum function. I'll do the first component for t\to\infty, to show you what's going on. We have

    x(t)=e^{at}(c_{1}\sin(bt)+c_{2}\cos(bt)).

    The trig functions are not going to either blow up or go to zero. Suppose a>0. Then the exponential blows up. Since we can't have that, the only option is if c_{1}=c_{2}=0. Otherwise, the x component blows up. If, on the other hand, a<0, then it doesn't matter what c_{1} and c_{2} are, the x component will go to zero.

    Conversely, let's say we are looking at t\to-\infty. The situation will be precisely the opposite of the previous case. a<0 means a blow-up unless c_{1}=c_{2}=0, and a>0 means the component goes to zero regardless of what c_{1} and c_{2} are.

    Does that help?
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Junior Member
    Joined
    Oct 2010
    Posts
    33
    yes thank you very much, i thought of that already!
    Follow Math Help Forum on Facebook and Google+

  4. #19
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    So you've got the final answer, then?
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Junior Member
    Joined
    Oct 2010
    Posts
    33
    I was wondering how the plot of this system would look like (depending on (a,b) )? But I dont know how to plot it in maple?
    Has anybody an idea?

    thx
    Follow Math Help Forum on Facebook and Google+

  6. #21
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Hmm. Your solution is a space curve in 3 dimensions, with parameter t, right? Any of those CAS's should be able to plot that, although I'm not sure how to do that in Maple. I could probably figure it out in Mathematica. Captain Black is your best bet for MATLAB. I don't know who is especially good at Maple on this forum. I would definitely consult the help manual for information on parametric plotting.
    Follow Math Help Forum on Facebook and Google+

  7. #22
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,373
    Thanks
    48
    I know a bit about Maple. What exactly are you trying to plot?
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. First order nonlinear system
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 7th 2011, 11:17 AM
  2. first order system
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 3rd 2010, 04:57 AM
  3. [SOLVED] Re-writing higher order spatial derivatives as lower order system
    Posted in the Differential Equations Forum
    Replies: 11
    Last Post: July 27th 2010, 08:56 AM
  4. Replies: 2
    Last Post: November 25th 2008, 09:29 PM
  5. System of second order ODE
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 15th 2008, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum