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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:

  1. Infinitely many solutions for some $f$.
  2. A unique solution in $\mathbb{R}$.
  3. No solution in $\mathbb{R}$ for some$ f$.
  4. 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.

  • 0
    Maybe $\frac{\mathrm d t}{f} = f(t) \mathrm d t$?2012-12-06

2 Answers 2