Arcgis 10.1 will not execute since i upgraded to windows 10. Is there a solution?
I would recommend you to either upgrade ArcGIS Desktop to ver. 10.3.1/10.4.x, or downgrade the OS to Win 8/7.
You should check system requirements prior to any upgrade... ArcGIS 10.4.x for Desktop system requirements—ArcGIS Help | ArcGIS for Desktop and you can check version 10.3 there as well ArcGIS 10.3.x for Desktop system requirements—Help | ArcGIS for Desktop
Versions < 10.3 aren't supported in windows 10, but I definitely will give a counter point to Jayanta's recommendation to downgrading your operating system. There is no point in downgrading an operating system, however, I never upgrade an old machine, it is rarely worth the time when/if things go wrong. If you are stuck because you don't have maintainence then there isn't much you can do.