Question: Say I have an expansion of terms containing functions `y[j,t]` and its derivatives, indexed by `j` with the index beginning at 0 whose independent variable are `t`, like so: 

`Expr = y[0,t]^2 + D[y[0,t],t]*y[0,t] + y[0,t]*y[1,t] + y[0,t]*D[y[1,t],t] + (y[1,t])^2*y[0,t] +` ... etc.

Now I wish to define new functions indexed by `i`, call them `A[i]`, that collect all terms from the expression above such that the sum of the indices of the factors in each term sums to `i`.

In the above case for the terms shown we would have for example

`A[0] = y[0,t]^2 + D[y[0,t],t]*y[0,t]`

`A[1] = y[0,t]*y[1,t] + y[0,t]*D[y[1,t],t]`

`A[2] = (y[1,t])^2*y[0,t]`

How can I get mathematica to assign these terms to these new functions automatically for all `i`?

Note: If there is a better way to be indexing functions also feel free to suggest.

Answer: 
Since [`Show`](http://reference.wolfram.com/language/ref/Show) uses the [`PlotRange`](http://reference.wolfram.com/language/ref/PlotRange) setting from the first plot, you can just set your plot range when defining the first plot:

```
p1=LogLogPlot[
    RO,
    {t,0.00001,0.05},
    PlotRange -> {{10^-5, 10^-4}, All},
    PlotStyle->{Purple}
];

Show[p1, p2]

```

or you can use a dummy plot with the desired plot range:

```
p0 = LogLogPlot[None, {t, 10^-5, 10^-4}];

Show[p0, p1, p2]

```

If you really want to set the [`PlotRange`](http://reference.wolfram.com/language/ref/PlotRange) using a [`Show`](http://reference.wolfram.com/language/ref/Show) option, than you need to realize that the [`Graphics`](http://reference.wolfram.com/language/ref/Graphics) objects produced by `p1` and `p2` don't know that "Log" scaling functions were used. So, you need to adjust the desired [`PlotRange`](http://reference.wolfram.com/language/ref/PlotRange) accordingly:

```
Show[p1, p2, PlotRange -> {Log @ {10^-5, 10^-4}, All}]

```
Your syntax is incorrect, it should be

```
Show[{p1,p2},PlotRange->{{x_min,x_max},{y_min,y_max}}]

```

If you want all in y, you can do:

```
Show[{p1,p2},PlotRange->{{10^(-5),10^(-4)},All}]

```