Results 1 to 5 of 5

Math Help - Particular Integral

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    164

    Particular Integral

    Hello, I was just wondering if there is a particular integral for a second-order linear inhomogeneous differential equation which is equal to lnx.

    I mean we are taught at university to use some particular integrals for some cases eg when we meet sinx, cosx, a polynomial, e^x but no one told us what to do if we find cotx, tanx, lnx, logx or any other function except of the three-four cases which are standard. Any reference for a complete list of particular integrals would be much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    The standard definition of the natural logarithm is \ln{x} = \int_{1}^{x}\frac{1}{t}\;{dt}.
    Is that what you were looking for? Or do you want to integrate \ln{x}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    164
    No, my question is what do we use as a particular integral when a second order linear inhomogeneous differential equation has as a right side the term lnx.
    I mean when the right side is e^x we use Ae^x, when it is x, we use Ax+b. If that term is lnx or tanx or cotx eg what do we use as a particular integral?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I don't think the guess-and-check method will work here. You'll have to do variation of parameters to solve problems like that. Warning: logarithms are not liable to give you pretty results. Here's an example.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2010
    Posts
    164
    Thank you very much Ackbeet. I am first year student and I am pretty interested in Differential Equations, that is why I asked. I think you know that in first year calculus we do not meet any other method except the particular integral! Thanks again for the information!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 31st 2010, 07:38 AM
  2. Replies: 1
    Last Post: June 2nd 2010, 02:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 01:52 PM
  4. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: September 16th 2009, 11:50 AM
  5. Replies: 0
    Last Post: September 10th 2008, 07:53 PM

Search Tags


/mathhelpforum @mathhelpforum