Existence of solution for IVP

1. Sep 12, 2010

sbashrawi

1. The problem statement, all variables and given/known data
suppose that h $$\in$$C(R) and f$$\in$$C(R^2) satisfies
|f(t,x)|$$\leq$$h(t) |x| for all (t,x) $$\in$$R^2. Show that for any point , the IVP : x' = f( t, x) x( $$\tau$$)=$$\varsigma$$
has a solution which exists for all t in R

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution