Results 1 to 5 of 5

Math Help - General solution...

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    34

    General solution...

    can someone help me get the general solution for this..I get confused about the derivative of x

    9d^2x/dt^2+6dx/dt+x=0
    ,X(-3)=2 ,dx/dt(-3)=1/2

    I get x(t)=(C1+C2t)e^-1/3t


    I cannot seem to get the answers for the initial conditions above..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Raidan View Post
    can someone help me get the general solution for this..I get confused about the derivative of x

    9d^2x/dt^2+6dx/dt+x=0 ,X(-3)=2 ,dx/dt(-3)=1/2

    I get x(t)=(C1+C2t)e^-1/3t

    I cannot seem to get the answers for the initial conditions above..

    I'm not sure that I understand. Is this what you have?

    9\frac{d^2x}{dt^2}+6\frac{dx}{dt}+x=0 where \frac<br />
{d^2x}{dt^2} is the second derivative of x with respect to t; and x is a function of t and x(-3)=2?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    34
    Quote Originally Posted by VonNemo19 View Post
    I'm not sure that I understand. Is this what you have?

    9\frac{d^2x}{dt^2}+6\frac{dx}{dt}+x=0 where \frac<br />
{d^2x}{dt^2} is the second derivative of x with respect to t; and x is a function of t and x(-3)=2?

    yes thats what I mean..hw would i do this
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2009
    Posts
    34
    oo and with the other intial condition x''(-3)=1/2
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Raidan View Post
    can someone help me get the general solution for this..I get confused about the derivative of x

    9d^2x/dt^2+6dx/dt+x=0 ,X(-3)=2 ,dx/dt(-3)=1/2

    I get x(t)=(C1+C2t)e^-1/3t

    I cannot seem to get the answers for the initial conditions above..
    So this is a 2nd order linear ODE with constant coeffeints so the auxillary equaiton is

    9m^2-6m+1=0 \iff (3m-1)(3m-1)=0 \iff (3m-1)^2=0

    So we have one repeated root. So we multiply by t to get the 2nd linearly independant solution.



    x(t)=c_1e^{\frac{t}{3}}+c_2te^{\frac{t}{3}}

    Now we can use IC to find the constants

    x'(t)=\frac{c_1}{3}e^{\frac{t}{3}}+\frac{c_2}{3}te  ^{\frac{t}{3}}+c_2e^{\frac{t}{3}}


    x'(-3)=\frac{1}{2}=\frac{c_1}{3}e^{-1}+\frac{c_2}{3}(-3)e^{-1}+c_2e^{-1} \iff 3e=2c_1-6c_2+6c_2 \iff c_1=\frac{3e}{2}

    x(-3)=2=\frac{3e}{2}e^{-1}+c_2(-3)e^{-1} \iff 4e=3e-6c_2\iff c_2=-\frac{e}{6}


    x(t)=\left( \frac{3e}{2}\right)e^{\frac{t}{3}}-\frac{e}{6}te^{\frac{t}{3}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. General Solution of a differential solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 11th 2010, 02:49 AM
  2. GENERAL SOLUTION f(x,t) please help
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: April 11th 2010, 04:36 PM
  3. Help w/ General Solution
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 19th 2010, 12:58 AM
  4. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: October 7th 2009, 01:44 AM
  5. find the general solution when 1 solution is given
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 4th 2009, 09:09 PM

Search Tags


/mathhelpforum @mathhelpforum