Results 1 to 7 of 7

Math Help - Solving partial of ODE to zero

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    8

    Solving partial of ODE to zero

    Hi guys, I have attached my derivation in the image below. Im not solving the ode, but I need a relationship in this equation. To solve that, I need to make the final part which is

    Code:
     [-B/1.101e-17+BN(t)-betaBN(t)]S(t)
    to zero, is there anyway that I could make it zero, any theorem that could solve this, I need this very urgently, I am almost solving my own relationship in my system.

    Please suggest what I can do. Thank you.
    Attached Thumbnails Attached Thumbnails Solving partial of ODE to zero-derivation.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well, as I see it, there are four ways to make that expression zero.

    1. B=0. Probably not acceptable, I'm guessing.
    2. S(t)=0. See above.
    3. N(t) is a constant, derived as follows:

    -\dfrac{B}{1.101\times 10^{-17}}+B\,N(t)-\beta\,B\,N(t)=0

    N(t)-\beta\,N(t)=\dfrac{1}{1.101\times 10^{-17}}

    N(t)=\dfrac{1}{(1.101\times 10^{-17})(1-\beta)}.

    4. Finally, you could have \beta defined as a function of t thus:

    -\dfrac{B}{1.101\times 10^{-17}}+B\,N(t)-\beta\,B\,N(t)=0

    -\dfrac{B}{1.101\times 10^{-17}}+B\,N(t)=\beta\,B\,N(t)

    \beta=\dfrac{-\frac{B}{1.101\times 10^{-17}}+B\,N(t)}{B\,N(t)}.

    Since there are no other variables, and all of the variables show up in the equation in a linear fashion, I see no other ways to make the expression zero.

    Hope this helps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2010
    Posts
    8
    Hi Ackbeet, thank you very much for the help, I have actually solved it, thanks a lot! May I ask you one more question? Attached is the differential equation that I want to solve both numerically and analytically, numerically done.

    But analytically what method could I use? There is so many methods in differential equations. Please advice on this.
    Attached Thumbnails Attached Thumbnails Solving partial of ODE to zero-new-ode.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by thavamaran View Post
    Hi Ackbeet, thank you very much for the help, I have actually solved it, thanks a lot! May I ask you one more question? Attached is the differential equation that I want to solve both numerically and analytically, numerically done.

    But analytically what method could I use? There is so many methods in differential equations. Please advice on this.
    The equation can be solved via an integrating factor.

    \displaystyle \frac{dz}{dt}-\left( \frac{-1+\beta}{\tau_n}{\right)z(t)=\Gamma\left( \frac{I(t)}{qv}\right)

    Your integrating factor would be

    \displaystyle e^{\int -\left( \frac{-1+\beta}{\tau_n}\right)dt}= e^{ -\left( \frac{-1+\beta}{\tau_n}\right)t}

    \displaystyle \frac{d}{dt}\left[ e^{ -\left( \frac{-1+\beta}{\tau_n}\right)t} \cdot z(t)\right]=e^{ -\left( \frac{-1+\beta}{\tau_n}\right)t}\Gamma\left( \frac{I(t)}{qv}\right)

    Now just integrate and solve for z(t)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2010
    Posts
    8
    Hi there, first of all thank you very much for the reply. I found earlier integrating factor is one of the method, but its rather very confusing, like in this case, I dont get why you picked \displaystyle {-1+\beta}{\tau_n} as the integrating factor? Thank you very much for the guidance.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2010
    Posts
    8
    Hi mate, thanks again, I found the solution for my earlier question! Thanks a lot, I will get back to you after the derivation. Thanks!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    For a first-order linear DE in standard form, which is

    y'+P(x)\,y=Q(x),

    the integrating factor is

    \displaystyle e^{\int P(x)\,dx}. That's how TheEmptySet picked the integrating factor.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Solving Partial Fractions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 23rd 2011, 06:34 PM
  2. solving partial fractions manually
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 13th 2011, 02:00 AM
  3. Solving an integral using partial fractions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 1st 2010, 05:31 PM
  4. Replies: 5
    Last Post: November 23rd 2009, 12:17 PM
  5. solving partial differential equations using complex numbers
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 11th 2009, 09:10 AM

Search Tags


/mathhelpforum @mathhelpforum