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: