Problem in solving ODE from NDSolve

Question

I have a problem in solving a type of ODE from NDSolve. Specifically I want to know the solution at time T (say T=50). The number of differential equations increases at each iteration. This equations involves one parameters, and I want the solution of the differential equations at each iteration.

T = 10;
nu = 0.2;
n = 5;

vars = Table[Subscript[x, j][t], {i, n}, {j, i}];

eqns = Table[{
    Subscript[x, j]'[t] == Subscript[x, j][t] (1 - Subscript[x, j][t] - nu Sum[Subscript[x, k][t] Boole[k != j], {k, i}]),
    Subscript[x, j][0] == 0.3},
  {i, n}, {j, i}
 ];

The variable eqns gives exactly the process of iteration that I need

sol = NDSolve[eqns, Table[Subscript[x, j], {i, n}, {j, i}], {t, 0, T}, DependentVariables -> vars]

But Mathematica gives the message

NDSolve::ndode: Input is not an ordinary differential equation. >>

I don't understand how to fix it. I believe it violates some operation NDSolve.

Answer 1

If you are attempting to solve ODEs one through five in sequence, one way to do so is

GraphicsGrid[{Table[s = NDSolve[eqns[[n]], vars[[n]], {t, 0, T}];
    Plot[Evaluate[vars[[n]] /. s], {t, 0, T}, PlotRange -> All], {n, 5}]}, 
    ImageSize -> Large]

Alternatively, the solutions can be presented in a single plot.

Show @@ Table[s = NDSolve[eqns[[n]], vars[[n]], {t, 0, T}];
    Plot[Evaluate[vars[[n]] /. s], {t, 0, T}, PlotRange -> All], {n, 5}]

Not surprisingly, all curves for each value of n coincide.