I want to convert the following into cartesion:

diff(r(t), t) = sin(Pi*r(t)), diff(theta(t), t) = 1

And then plot the phase portrait.

Could someone help me with this?

How do i solve differential equations using Maple.

For example:

dx/dt+(1-cos(t))*x = exp(sin(t))

I've written a procedure to generate a Farey sequence F_N of order N where b=1,2,...,N & a=0,1,...b; as follows:

restart:
> farey:= proc(N::posint)
> local a,b,L:
> for b to N do:
>   for a to b do:
>   if a<=b then L:=sort([op({seq(seq(a/b,a=0..b),b=1..N)})]):
>   end if:
>  end do:
> end do:
> print(F[N]=L);
> end proc:

I decided to repost this as the previous one went crazy.......

I'm trying to construct an iterative procedure NR1(f,x0,N) where f is a function, x0 is an initial estimate (which can be complex) and N the number of iterates.

Given:  x_k+1=x_k - f(x_k)/f'(x_k), k=0,1,2....,

Now for example by defining f:= x-> x^2-2 and inputting x₀=1 and N=10 i should be able to check that my procedure calculates sqrt(2) correctly.

This is what i've got so far.....

I'm trying to construct an iterative procedure NR1(f,x0,N) where f is a function, x0 is an initial estimate (which can be complex) and N the number of iterates.

Given:  x_k+1=x_k - f(x_k)/f'(x_k), k=0,1,2....,

Now for example by defining f:= x-> x^2-2 and inputting x₀=1 and N=10 i should be able to check that my procedure calculates sqrt(2) correctly.

This is what i've got so far.....