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Finding the differential equation (initial value problem)

  1. Apr 17, 2013 #1
    Homework problem for nonlinear dynamics.


    Let us write xλ(t) for the solution of the initial value problem
    [itex]\dot{x}[/itex] = f(x) & x(0) = λ
    where f is continuously differentiable on the whole line and f(0) = 0.
    a) Find the differential equation for [itex]\frac{∂x_{λ}}{∂λ}[/itex](t)


    I'm a little confused about where to begin, so any sort of push in the right direction would be appreciated. Also, what does the λ subscript mean?
     
    Last edited: Apr 17, 2013
  2. jcsd
  3. Apr 18, 2013 #2

    tiny-tim

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    hi djh101! :smile:
    xλ(t) is the solution to dx/dt = f(x) with initial condition x(0) = λ

    hint: what can you say about xλ+dλ(t) - xλ(t) ? :wink:
     
  4. Apr 18, 2013 #3
    xλ+dλ - xλ = x = ∂xλ?
     
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