This is from my practice problems for an exam on friday.
Here's what I have so far:
1.
A) Plug in x=t and t=t and x`=1 into the equation to get (t)(1)=(t). Thus x(t)=t is a solution. I'm not sure what maximal interval of existence means. This solution exists everywhere where t doesn't equal zero, because x`=x/t. Is that all I have to say? Or is it something like (0, infinity)?
B) Another solution by inspection is x(t)=0. This is easy to verify graphically, or just logically. No problems there.
C) Wouldn't this invalidate the existence theorem? Because there's no rectangle R you can draw containing (0,0) where x` is continous? Is just saying that enough, or is more needed?
Thanks in advance.