# Finding the differential equation (initial value problem)

1. Apr 17, 2013

### djh101

Homework problem for nonlinear dynamics.

Let us write xλ(t) for the solution of the initial value problem
$\dot{x}$ = f(x) & x(0) = λ
where f is continuously differentiable on the whole line and f(0) = 0.
a) Find the differential equation for $\frac{∂x_{λ}}{∂λ}$(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. Apr 18, 2013

### tiny-tim

hi djh101!
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) ?

3. Apr 18, 2013

### djh101

xλ+dλ - xλ = x = ∂xλ?