problem with uniqueness of IVP

[kochibacha]

Are these statements correct, if not could you give me an example

1. If solution of IVP is non-unique then there are infinitely many solutions
[h=1][/h]in short, if the solution to the IVP has at least 2 solutions then there are infinitely many solutions to this IVP

2.there are none IVP first order ODE's with finite solutions

for example there are no such IVP's that have only 2 or 3 solutions it must be either one or infinite

3. there is no first order linear ODE's that have more than 1 solution for each different initial conditions if the solution exists

 

[HallsofIvy]

Based on what? What do you know or can use? I would think that the "existence and uniqueness" theorem, specialized for linear equations would prove most of these.

When you say "finite solutions" do you mean y(x) is finite for all finite x or that there are a finite number of solutions?

 

[kochibacha]

Based on what? What do you know or can use? I would think that the "existence and uniqueness" theorem, specialized for linear equations would prove most of these.

When you say "finite solutions" do you mean y(x) is finite for all finite x or that there are a finite number of solutions?

finite number of solutions , sorry for ambiguous writing