Extract fields of a specific Data Type from a sObject

Schema.DescribeSObjectResult objectDescribe = Case.SObjectType.getDescribe();
Map<String, Schema.SObjectField> fieldMap = objectDescribe.fields.getMap();

for( String fieldName : fieldMap.keySet() ) {
    Schema.SObjectField field = fieldMap.get(fieldName);
    Schema.DescribeFieldResult fieldDescribe = field.getDescribe();
    
    if (String.valueOf(fieldDescribe.getType()) == 'DATETIME') {
        System.debug(fieldName);
    }
}