Need help finding birth records in OHIO

My mother gave birth to my brother in approx. 1974 in Ohio, he went to live with his fathers mother and I have no way of finding him. I know that his name was Rayvon (or Rayvonne) I am not sure of the spelling, and that he is african-american. My mothers name was Florence Jean Rush, and her DOB was 1/11/1949. He might of been given his fathers last name, I don't know that information all I know is his first name was Richard. I was born in Lima, Ohio and I believe he could have been born around there, however I know that his family may reside in Cleveland, Ohio. Is there anyway to look up records simply by my mothers name so I can find the true spelling his first name and his last name if it is not Rush? He was not adopted so his birth records should not be sealed, I just have no idea how to find him. Any information would be so appreciated, I am located in Los Angeles, CA so finding out anything is difficult.Please contact me at Akilizaire@aol.com