In order to get a search box for your website that uses DuckDuckGo, you can use the following snippet.
<form target="_blank" method="get" action="https://duckduckgo.com">
<!-- Search box -->
<input name="q" type="text" placeholder="Search terms" />
<!-- The website to search -->
<input value="gkbrk.com" name="sites" type="hidden" />
<!-- Region for localization, optional -->
<input value="uk-en" name="kl" type="hidden" />
</form>
@article{yaltirakliwikiduckduckgosearchbox, title = "DuckDuckGo Search Box", author = "Yaltirakli, Gokberk", journal = "gkbrk.com", year = "2022", url = "https://www.gkbrk.com/wiki/DuckDuckGoSearchBox/" }
Gokberk Yaltirakli, "DuckDuckGo Search Box", September, 2022. [Online]. Available: https://www.gkbrk.com/wiki/DuckDuckGoSearchBox/. [Accessed Sep. 24, 2022].
Yaltirakli, G. (2022, September 24). DuckDuckGo Search Box. https://www.gkbrk.com/wiki/DuckDuckGoSearchBox/
Gokberk Yaltirakli, DuckDuckGo Search Box, GKBRK.COM (Sep. 24, 2022), https://www.gkbrk.com/wiki/DuckDuckGoSearchBox/