Results 1 to 4 of 4

Math Help - Need help with elimination method

  1. #1
    Member diddledabble's Avatar
    Joined
    Jul 2009
    Posts
    80

    Need help with elimination method

    Okay, I need a plain english explaination of how to go about solving problems like this. This one was given as an example in my textbook but the author skipped too many steps, so you won't spoil anything by answering it.
    Using the elimination method, find a general solution where differentiation is with respect to t.

    x' = 3y
    y' = 2x - y
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by diddledabble View Post
    Okay, I need a plain english explaination of how to go about solving problems like this. This one was given as an example in my textbook but the author skipped too many steps, so you won't spoil anything by answering it.
    Using the elimination method, find a general solution where differentiation is with respect to t.

    x' = 3y
    y' = 2x - y
    Differentiate the second equation again:

    y''=2x'-y'

    Now substitute from the first into this to get:

    y''=6y-y'

    which is a second order constant coefficient linear homogeneous ODE and hence can be solved with no trouble.

    Solve it, now substitute the solution back into the second equation y'=2x-y to find x.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member diddledabble's Avatar
    Joined
    Jul 2009
    Posts
    80

    Check my work

    Okay, so from what Captain said and using my book I got this...
    Auxiliary equation
    r^2+r-6=0
    (r+3)(r-2)=0 so r= -3, 2

    y(t)=c1e^(-3t)+c2e^(2t)
    y'(t)=-3c1e^(-3t)+2c2e^(2t)

    Subbing back into y'=2x-y
    -2c1e^(-3t)+3c2e^(2t)=2x
    x(t)=-c1e^(-3t)+ (3/2)c2e^(2t)

    Also if someone can type these in LaTex I would appreciate it. I tried and it didn't work out very well. Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by diddledabble View Post
    Okay, so from what Captain said and using my book I got this...
    Auxiliary equation
    r^2+r-6=0
    (r+3)(r-2)=0 so r= -3, 2

    y(t)=c1e^(-3t)+c2e^(2t)
    y'(t)=-3c1e^(-3t)+2c2e^(2t)

    Subbing back into y'=2x-y
    -2c1e^(-3t)+3c2e^(2t)=2x
    x(t)=-c1e^(-3t)+ (3/2)c2e^(2t)

    Also if someone can type these in LaTex I would appreciate it. I tried and it didn't work out very well. Thanks!
    Translated into LaTeX:

    Okay, so from what Captain said and using my book I got this...
    Auxiliary equation

    r^2+r-6=0
    (r+3)(r-2)=0 so r= -3, 2

    y(t)=c_1\;e^{-3t}+c_2\;e^{2t}
    y'(t)=-3c_1\;e^{-3t}+2c_2\;e^{2t}

    Subbing back into y'=2x-y

    -2c_1\;e^{-3t}+3c_2\;e^{2t}=2x
    x(t)=-c_1\;e^{-3t}+ (3/2)c_2\;e^{2t}

    Also if someone can type these in LaTex I would appreciate it. I tried and it didn't work out very well. Thanks!

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 12th 2011, 10:03 PM
  2. Elimination method
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 22nd 2011, 06:18 AM
  3. Elimination Method
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 14th 2010, 10:53 PM
  4. The Method of Elimination
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 6th 2009, 07:24 AM
  5. Elimination Method
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 25th 2007, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum