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- TL;DR Summary
- I am trying to find if there is a way to prove the existence and uniqueness of a solution

to a first order ODE on an interval including infinity.

I am trying to find a way to prove that a certain first order ode has a unique

solution on the interval (1,infinity). Usually the way to do this is to show that

if x' = f(t,x) (derivative with respect to t), then f(t,x) and the partial derivative with respect to f are continuous.

However, this would show that a solution exists only on an interval

Is there any way to show that a solution exists on the entire interval?

solution on the interval (1,infinity). Usually the way to do this is to show that

if x' = f(t,x) (derivative with respect to t), then f(t,x) and the partial derivative with respect to f are continuous.

However, this would show that a solution exists only on an interval

*inside*(1,infinity).Is there any way to show that a solution exists on the entire interval?