If Lutheran, Trinity Cemetery
5210 Mt Elliott St Detroit, MI 48211
The Michigan County death records from 1921-1951 were indexed last year and are in the process of final checking. The cemetery is general listed. When that is finished they will be viewable at the Mormon Church's website www.FamilySearch.org
For an obituary from 1943, the main Detroit Public Library has the three Detroit newspapers and will do a look-up and make a copy for a fee.http://www.detroit.lib.mi.us/specialservice/obituary-search
If her husband died between 1897 and 1920 in Michigan, look for him at www.SeekingMichigan.org
under the death records. It should show where he was buried.