Is it permissible to share in a single animal for 'aqiqah and udhiyah, while there is a partner intending only udhiyah, and how would the shares be divided in this case?

Scholars have differed regarding the permissibility of 'aqiqah with animals other than sheep. The majority opinion permits it with cattle and camels. They then differed on the permissibility of sharing in a camel or a cow, and the apparent (stronger) opinion is that it is permissible, which is the view of the Shafi'is. Based on this, two-sevenths of a cow would suffice for both the 'aqiqah and the udhiyah if you intend to perform the 'aqiqah for one newborn and offer a sacrifice.