How to declare a list of functions in ODE system solving?

Questions
1

For instance a ODE system of two unknown functions:
x(t_):={x1(t),x2(t)};
DSolve[x’[t]==a.x(t),x(t),t]

Now, suppose that instead of two, I have 1,000,000 unknown functions. How do I write x(t_):={x1(t),x2(t),…,x1000000(t)}?

2

In[6]:= xx[t_] = Through[Array[x, 3][t]]

Out[6]= {x[1][t], x[2][t], x[3][t]}
3

Worked. Thanks!

4

How about this..

xx[t_]=Table[x[i][t], {i, 3}]
{x[1][t], x[2][t], x[3][t]}
5

In[31]:= x[#][t] & /@ Range[3]

Out[31]= {x[1][t], x[2][t], x[3][t]}
6

Subscript[x, #][t] & /@ Range[3]

7

ToExpression[“x” <> ToString[#] <> “[t]”] & /@ Range[3]

 {x1[t], x2[t], x3[t]}
8

x #[t] & /@ Range@3
{x 1[t], x 2[t], x 3[t]}

9

I don’t think that would work as a list of functions

In[5]:= x #[t] & /@ Range@3

Out[5]= {x 1[t], x 2[t], x 3[t]}

In[6]:= InputForm[%]

Out[6]//InputForm=
{x*1[t], x*2[t], x*3[t]}