Math Forum / Math Software / Mathematica / July 2009

Hi, there.

I am new to mathematica and recently I am intrigued by the convenience of
NDSolve function, since there is no need to write the Runge-kutta like
functions myself to solve ODEs. However, if what I want to solve is a list
of equations expressed in a loop way, I have no idea how to express it.

For example, a set of simple equations are:
Subscript[y, i]'[x]  = Subscript[y, i][x] Cos[x + Subscript[y, i][x]] + i,
where i=1,2,...,N;

if N is small, of course I can write the equations separately, i.e.
Subscript[y,1]'[x]  = Subscript[y,1][x] Cos[x + Subscript[y,1][x]] + 1
Subscript[y,2]'[x]  = Subscript[y,2][x] Cos[x + Subscript[y,2][x]] + 2
...
Subscript[y,N]'[x]  = Subscript[y,N][x] Cos[x + Subscript[y,N][x]] + N
But if N is large, this method seems clumsy, so I would like to express this
kind of "loop" equations in a neat way.

I have tried to nest "do" or "for" to control this loop, but the problem is
that they can not be incorporated into the NDSolve function. Does anyone
have a better solution?

Best regards and thanks in advance.

Haibo