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Find 'k' for x(t)=k is solution for diff eq

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the value of k for which the constant function x(t)=k is a solution of the differential equation 6t^5dx/dt+7x−4=0.

    3. The attempt at a solution

    I have tried this several ways but no luck, here is one of my attempts,

    solve for dx/dt,

    dx/dt = (4-7x)/6t^5

    take the integral,

    x(t) = (1/6t^5)(4x-7x^2/2)

    and that doesn't help :P
    I am sure as usual I am missing something straightforward but I don't see it.
     
  2. jcsd
  3. Sep 2, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    You have ##x(t) = k## therefore ##x'(t) = 0##.

    Plugging those in yields :

    ##(6t^5)(0) + 7k − 4= 0##

    I'm sure that you got this now. It's the same concept as in your prior thread.
     
  4. Sep 2, 2013 #3
    You know....
    At least missing these types of things typically only happens once.

    Thanks again!
     
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