How do I find a node knowing its URL? I need to rename the node home-care/vids into home-care/product-solutions. The trouble is that I can't find home-care/vids in the dashboard of this relatively big site.

How can I find it?

I have even done a MySQL database search but results are not helpful for me.
The easiest way is almost always to visit the page you want to change, and hit the "Edit" button among the tabs.

However, sometimes this may not be practical for whatever reason. SQL-queries below:

D6

SELECT src FROM url_alias WHERE dst = 'home-care/vids';

D7

SELECT source FROM url_alias WHERE alias = 'home-care/vids';

You may in both version want to add AND language = if your site is multilingual.