A custodial parent or guardian of a minor child or children or a child or children who have reached 18 years of age may proceed in the same manner, and under the same circumstances as provided in section 1, against the noncustodial parent for the support of the child or children. The order of support shall provide only for the support of the child or children, and the burden of proof shall be the same as provided in section 2. This section applies only to legitimate, legitimated, and lawfully adopted minor children and, subject to section 5b of the support and parenting time enforcement act, 1982 PA 295, MCL 552.605b, children after they reach 18 years of age.