A home rule charter may be amended by one of the following methods:
1. The council, by resolution, may submit a proposed amendment to the voters at a special city election, and the proposed amendment becomes effective if approved by a majority of those voting.
2. The council, by ordinance, may amend the charter. However, within thirty days of publication of the ordinance, if a petition valid under the provisions of section 362.4 is filed with the council, the council must submit the ordinance amendment to the voters at a special city election, and the amendment does not become effective until approved by a majority of those voting.
3. If a petition valid under the provisions of section 362.4 is filed with the council proposing an amendment to the charter, the council must submit the proposed amendment to the voters at a special city election, and the amendment becomes effective if approved by a majority of those voting.