When the ordinance provided for in the preceding section has been duly passed, the city council shall cause to be entered an order to such effect on the minutes of the council. From and after the entry of such order, such territory shall cease to be part of the city; provided, that the city council may exercise its own discretion with reference to discontinuing any part of such territory and in no case shall any territory be discontinued, except on the application of the owner or owners of such territory and where the metes and bounds of the territory that is sought to be discontinued are clearly set forth in such application; provided further, that all applications for the discontinuance of any territory shall be in writing as provided in this section, and approved by the city engineer’s and the city attorney’s departments. (Code 1941, Art. 29-2)