Results 1 to 2 of 2

Thread: Determine r for Explicit Formula

  1. #1
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1

    Determine r for Explicit Formula

    Determine what the value(s) of r has to be in order to find explicit formulas (that is, formulas without integrals) for solutions to $\displaystyle \displaystyle \frac{dy}{dt}=t^ry+4$. Determine what the general solutions are for each value of $\displaystyle r$.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,002
    Thanks
    1
    Just by looking at it, $\displaystyle -1\leq{r}\leq{0}$ have a few good ones.

    Do you see why, say 2, will not work?.

    If r=2, then you have an integrating factor of $\displaystyle t^{2}$.

    Then $\displaystyle e^{\int{t^{2}}dt}=e^{\frac{t^{3}}{3}}$

    Which is not integrable by elementary means.

    Actually, $\displaystyle e^{\int{t^{r}}}dt=e^{\frac{t^{r+1}}{r+1}}$ are generally not easily integrated.
    Trying to integrate $\displaystyle \int{e^{\frac{t^{r+1}}{r+1}}}dt$ can be a booger.

    Then you have for r=0 $\displaystyle e^{\int{dt}}=e^{t}$

    If r=-1, then $\displaystyle e^{\int\frac{1}{t}dt}=t$

    And so on. Just something to think about. See if you can find others in the interval that will or will not work.
    Last edited by galactus; Oct 13th 2007 at 03:03 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Explicit Sequence Formula
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 24th 2010, 07:33 PM
  2. Replies: 1
    Last Post: Nov 6th 2009, 03:57 AM
  3. Replies: 0
    Last Post: Nov 5th 2009, 11:41 AM
  4. explicit formula
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 19th 2008, 12:23 PM
  5. Finding the explicit formula and the 100 term
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Nov 26th 2007, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum