The preferred way, using JDBC Metadata...
If you have access to a JDBC Connection, you can retrieve the vendor of database server fairly easily without going through an SQL query.
Simply check the connection metadata:
string dbType = connection.getMetaData().getDatabaseProductName();
This will should give you a string that beings with "MySQL" if the database is in fact MySQL (the string can differ between the community and enterprise edition).
If your bug is caused by the lack of support for one particular type of statement which so happens that MySQL doesn't support, you really should in fact rely on the appropriate metadata method to verify support for that particular feature instead of hard coding a workaround specifically for MySQL. There are other MySQL-like databases out there (MariaDB for example).
If you really must pass through an SQL query, you can retrieve the same string using this query:
SELECT @@version_comment as 'DatabaseProductName';
However, the preferred way is by reading the DatabaseMetaData object JDBC provides you with.