Results 1 to 4 of 4

Math Help - GENERAL SOLUTION f(x,t) please help

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    2

    Unhappy GENERAL SOLUTION f(x,t) please help

    hello,
    im having difficulty answering this question, please could somebody spare sometime answering it.. it starts off an exam paper and is putting me off the whole thing..

    wats da general solution of

    (∂^2/∂x∂t )f(x,t)=xt

    thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2009
    Posts
    145
    Do you mean  \frac{\delta^2 f}{\delta x \delta t} = xt ? In which case, integrating once with respect to t,

     \frac{\delta f}{\delta x} = \frac{xt^2}{2} + A'(x) where A is arbitrary. Integrating again with respect to x we get

     f(x,t) = \frac{(xt)^2}{4} + A(x) + B(t) With B also being arbitrary.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    2

    Arrow A'(x)??

    thank-you for ur reply.. not too sure why you have got A'(x) in the first part.. but then for the B arbitary constant you have B(t), shouldnt this be B'(t) too. I underdstand why A'(x) becomes A(x), or maybe i have not got the concept wright????

    thanks in advance
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2009
    Posts
    145
    Okay, so, when we integrate with respect to t, we have to include an arbitrary function of x. You can call this function A or A', because it's completely arbitrary what it is anyway. We choose A' because we know that we still have to integrate with respect to x, which will yield just A.

    After integrating with respect to x, we need to include an arbitrary function of t. We choose B(t) instead of B'(t) because we aren't going to be integrating again. You could have chosen to call it B' and you'd still be correct - it's an arbitrary function anyway. I hope that clears up my choices here.
    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, 03:49 AM
  2. General Solution
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 8th 2010, 10:06 PM
  3. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: October 7th 2009, 02:44 AM
  4. find the general solution when 1 solution is given
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 4th 2009, 10:09 PM
  5. General solution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 4th 2008, 12:38 PM

Search Tags


/mathhelpforum @mathhelpforum