Results 1 to 4 of 4

Math Help - Differential Equation Problem

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    30

    Differential Equation Problem

    I can't remember Diff EQ to save my life.

    but I have a'(t)=a(t)*a'(0) where a'(0) is constant


    my book does

    a'(t)/a(t) = d/dt *ln[a(t)] = a'(0)

    then they integrate both sides from T to 0 and get

    ln[a(t)] = t*a'(0)

    we know that if t = 1 ten a(1) = 1 + i, and i some interest rate


    then we know ln (1+i) = a'(0)


    so basically you get a(t)=(1+i)^t


    but I thought from Diff Eq any function of the forum
    y'=c*y would give you y =Ce^xt

    so how come this one doesn't?
    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 Jrb599 View Post
    I can't remember Diff EQ to save my life.

    but I have a'(t)=a(t)*a'(0) where a'(0) is constant


    my book does

    a'(t)/a(t) = d/dt *ln[a(t)] = a'(0)

    then they integrate both sides from T to 0 and get

    ln[a(t)] = t*a'(0)

    we know that if t = 1 ten a(1) = 1 + i, and i some interest rate


    then we know ln (1+i) = a'(0)


    so basically you get a(t)=(1+i)^t


    but I thought from Diff Eq any function of the forum
    y'=c*y would give you y =Ce^xt

    so how come this one doesn't?
    You have:

    <br />
a(t)=(1+i)^t=e^{[\ln(1+i)]t}<br />

    which is of the form:

    <br />
a(t)=C e^{\lambda t}<br />

    which is the general form of the solution to

    <br />
y'=\lambda y<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    30
    Are you able to show the steps, or is there not enough information?
    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 Jrb599 View Post
    Are you able to show the steps, or is there not enough information?
    You have:

    Because for any posive number k we have k=e^{\ln(k)}, so if we put k=(1+i) we may rewrite your solution:

    <br />
a(t)=(1+i)^t=e^{[\ln(1+i)]t}<br />

    Now put C=1, and x= \ln(1+i) , then:

    <br />
a(t)=Ce^{x t}<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  2. Differential Equation Problem 2
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 28th 2009, 12:31 AM
  3. Differential equation problem
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 22nd 2009, 02:25 AM
  4. differential equation problem - help please!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 24th 2008, 07:59 AM
  5. Differential Equation Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 23rd 2007, 05:30 AM

Search Tags


/mathhelpforum @mathhelpforum