Question: You have a differential equation y'[x] = f[x, y[x]]. If you have a formula for f[x, y] and you start with y[0] = 1, then
You have a differential equation
y'[x] = f[x, y[x]].
If you have a formula for f[x, y] and you start with
y[0] = 1,
then you can use NDSolve to plot out a function y[x] with
y[0] = 1 and y'[x] = f[x, y[x]].
On the other hand if you start with y[0] = 2, then you can use NDSolve to plot out a function y[x] with
y[0] = 2 and y'[x] = f[x, y[x]].
The question here is: Can the plots of these two solutions ever cross over each other like this:
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