Voy a hacer mi trabajo de literatura de la forma que yo quiera.
Yes, with the subjunctive, the speaker is not thinking of a specific way to do his literature job - they mean the way they want to do it "whichever that way might be". Here is a lesson that will help.
As a contrast with the indicative, imagine this scenario: two people are playing cards and they have two different opinions on what the rules are, so each of them explains their own rules to apply while playing. Then as they don't get to an agreement on the rules, one of them says: "Vamos a jugar como yo quiero."
He is using here the indicative because he is referring to that specific way he has already explained (his own rules), so it's information that they already know.
I hope this helps clarify.
It's subjunctive because "the form that I want" is an open expression. It is nothing specific, anything that implies "however I want" would be in the subjunctive form.
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