There probably isn't a plug and play solution, since every database is different.
Your index likely shows the latest entries, right?
Assuming your site is using a SQL database:
Copy the entire index page, and just modify the SQL command to only list those rows matching the search query, instead of listing the latest rows.
Some basic info on SQL WHERE and LIKE commands:
https://www.w3schools.com/sql/sql_like.asp
Edit: be sure to sanitize the user input.