The department of youth services, in the manner provided in this chapter and Chapter 2151 of the Revised Code, may transfer to a foster care facility certified by the department of job and family services under section 5103.03 of the Revised Code, any child committed to it and, in the event of a transfer of that nature, unless otherwise mutually agreed, the department of youth services shall bear the cost of care and services provided for the child in the foster care facility. A juvenile court may transfer to any foster facility certified by the department of job and family services any child between twelve and eighteen years of age, other than a psychotic child or a child with an intellectual disability, who has been designated a delinquent child and placed on probation by order of the juvenile court as a result of having violated any law of this state or the United States or any ordinance of a political subdivision of this state.