Cannot change Preferred Search Center in My Site Settings - SharePoint 2013

You can't change the search center for SharePoint My Site from the UI. The solution would be in powershell.

Open and run SharePoint Management Shell as Administrator.

Run next command

$ssa = Get-SPEnterpriseSearchServiceApplication "Search Service Application"
$ssa.SearchCenterUrl = "http://url/site/searchcentername/Pages/"
$ssa.Update

"Search Service Application" - name of  Search Service Application

When done do an IIS reset and try searching from your mysite.