I am afraid that the above answer is wrong.
To oxidise a secondary alcohol, you need to heat under reflux. While to partial oxidise a primary alcohol in order to get aldehydes, you just need to warm it. If you heat primary alcohol under reflux, you will get carboxylic acid, which will not react with Tollen's reagent.
Well, you can still do the above test, but test the end products with blue litmus paper or any tests that can identify a carboxylic acid.
Alternatively, warm the solutions with oxidising agent and test it with Tollen's reagent. The primary alcohol will form a silver precipitate but the secondary will form nothing as it didn't even get oxidised.