Solution
= Solution
For $h=f_1-f_2$, $h\prime=\sqrt{1+x}(f_1+f_2)h$ and $h(0)=0$. On every compact subinterval the coefficient is continuous, so <Gronwall inequality> gives $h=0$; hence equality holds throughout $[0,a)$.
= Solution
For $h=f_1-f_2$, $h\prime=\sqrt{1+x}(f_1+f_2)h$ and $h(0)=0$. On every compact subinterval the coefficient is continuous, so <Gronwall inequality> gives $h=0$; hence equality holds throughout $[0,a)$.