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Math Help - Let n be the smallest digit in your K-Number that is greater than 1 and?

  1. #1
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    Question Let n be the smallest digit in your K-Number that is greater than 1 and?

    Let n be the smallest digit in your K-Number that is greater than 1 and consider the ODE



    dx/dt = (1/n) cos(t - nx)

    Investigate the possibility of straight line solutions and discuss the asymp-
    totic behaviour of x(t). (Your investigation and discussion must contain
    rigorous mathematics )

    please help..
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  2. #2
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    Quote Originally Posted by hazeleyes View Post
    Let n be the smallest digit in your K-Number that is greater than 1 and consider the ODE



    dx/dt = (1/n) cos(t - nx)

    Investigate the possibility of straight line solutions and discuss the asymp-
    totic behaviour of x(t). (Your investigation and discussion must contain
    rigorous mathematics )

    please help..
    I am assuming that you k-number is your student id number. I will use 5 in this example.

    If we "guess" a linear solution then

    \displaystyle x(t)=mt+b \implies \frac{dx}{dt}=m

    If we put this into the ODE we get

    \displaystyle m=\frac{1}{5}\cos\left(t-5(mt+b) \right)

    First notice that the only way the trig function can be constant is if \displaystyle m=\frac{1}{5} This gives

    \displaystyle \frac{1}{5}=\frac{1}{5}\cos\left(-5b \right)

    This will require

    \displaystyle -5b= \cos^{-1}(1) \iff -5b=2n\pi,n \in \mathbb{Z}
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  3. #3
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    Thank you so much!!! it helps a lot!!!
    I'm wondering does it makes different if 'n' is an even number in the process? thanks
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    Behold, the power of SARDINES!
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    Quote Originally Posted by hazeleyes View Post
    Thank you so much!!! it helps a lot!!!
    I'm wondering does it makes different if 'n' is an even number in the process? thanks
    n does not really have anything to do with the problem. If you replace 5 with n in my post and follow the same argument you will see that nothing changes!
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