Results 1 to 5 of 5

Math Help - first order differential equation from variational calculus problem has me stumped!

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    40

    first order differential equation from variational calculus problem has me stumped!

    This arises when solving the problem of Dido,

    \frac{\dot x}{\sqrt{1+\dot x^2}} = -\frac{t}{\lambda} + C, where C and \lambda constant

    They mention that it can be solved by direct integration or by using the substitution \dot x =tan(\alpha).

    The solution is given as circles of the form (\frac{t}{\lambda}-d)^2+(\frac{t}{\lambda}-k)^2 = 1 where d and k are constants of integration.

    I don't know how to deal with that many differentials of x on the same side of the equation! I need some guidance here !
    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, what do you get on the LHS when you do the indicated substitution?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    40
    i get sin ? Let me work on it a little more, thanx for the tip !
    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
    Sounds good so far. Keep going!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2010
    Posts
    5
    First of all substitute z for (C - t/λ) on the R.H.S. and don't forget to change from dx/dt
    to dx/dz on the L.H.S. Then solve for dx/dz , to get it as a function of z.Now integrate both sides using tables....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2nd order differential equation problem
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: August 27th 2011, 12:56 PM
  2. Second Order differential equation problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 8th 2010, 12:21 AM
  3. Problem with first order separabel differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 9th 2009, 05:29 PM
  4. calculus first order differential equation~
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 8th 2009, 07:24 PM
  5. First order differential equation problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 2nd 2009, 12:49 PM

Search Tags


/mathhelpforum @mathhelpforum