The situation you have described is a common occurrence among startups these days. As has been specified, there is no legal requirement for you to provide equal equity to your co-founder and what you provide him is completely dependent on negotiations and the familiarity between you two. However, do note that a lot of start-ups have faced issues, including funding issues, if the founders are not absolutely or completely involved in the start-up but have a significant equity stake (and therefore, control) in the start-up. Given that you would be taking on the lion’s share of the work, you should consider entering into a founder’s agreement and after incorporating a company, you could consider vesting certain shares to your co-founder depending on his involvement in the company, and such vesting can be for a limited notional amount and quantity of shares. Absent a vesting schedule, there may be a likelihood that a non-working co-founder may jeopardize the growth of the company. Thus, a vesting schedule ensures continued dedication and involvement with the start-up without a significant downside. The contours of the agreements, the commercials and procedures can all be subject to negotiation between you and your co-founder.
There is no legal requirement as to how much equity you should give your friend. In order to incorporate a company you would need two shareholders but that can be achieved through your spouse/ other relatives/ friends. As to how much equity you should both hold is an item which you should negotiate with your co founder. In the event that you think he will not be involved in the project you can offer him a 10%-20% stake. However please ensure that all the intellectual property in the product vests with you. You may need an IP assignment from him. This requirement varies from case to case.