Consider the initial value problem $y’(t)=f(t)y(t), \;y(0)=1$ where $f:\mathbb{R}\to\mathbb{R}$ is continuous. Then this initial value problem has:
- Infinitely many solutions for some $f$.
- A unique solution in $\mathbb{R}$.
- No solution in $\mathbb{R}$ for some$ f$.
- A solution in an interval containing $0$, but not on $\mathbb{R}$ for some $f$.
Can anyone help me finding which of the options are correct? Thanks.