Learn Hardcore German: Die provisorische Lösung funktioniert nur kurz, danach nehmen wir den festen Plan. - The temporary solution works only briefly; afterwards we use the solid plan.

Both are possible. Die points to a specific, known stopgap solution (already mentioned or contextually clear). Eine would mean “a” temporary solution in general. In the given sentence, using die suggests the speakers have a particular stopgap in mind; using eine would generalize more.

Why does provisorische end in -e here?

Because Lösung is feminine and in the nominative singular, and it’s preceded by the definite article die. After a definite article in feminine nominative, the adjective ending is -e: die provisorische Lösung. Compare:

Feminine nominative: die provisorische Lösung
Masculine nominative: der feste Plan
Masculine accusative: den festen Plan → adjective ending becomes -en: den festen Plan

Could I use vorläufig instead of provisorisch? Any nuance difference?

Yes, but there’s a nuance. provisorisch suggests “makeshift/temporary patch,” often not ideal. vorläufig means “for the time being, until further notice,” and can sound a bit more official. Another near-synonym is behelfsmäßig (“improvised/makeshift”), which emphasizes the stopgap nature even more.

Why is funktioniert used instead of arbeitet or geht/klappt?

funktionieren is the standard verb for “to function/work (as intended)” for things, ideas, solutions: Die Lösung funktioniert.
arbeiten means “to work (as a person)” or “operate” for machines, not for abstract solutions: Die Maschine arbeitet, but not Die Lösung arbeitet.
klappen is colloquial for “to work out/succeed”: Es klappt.
gehen colloquially can mean “to work”: Das geht, but it’s informal and context-dependent.

So funktioniert is the precise, neutral choice here.

What exactly does nur kurz mean here?

It means “only for a short time/for a short while.” It speaks about duration, not physical length. Synonyms/paraphrases:

nur kurzzeitig
nur für kurze Zeit
nicht lange Slightly different nuance: nur kurz is everyday and concise; kurzzeitig is a bit more formal.

Why is there a comma before danach? Is danach a conjunction?

German requires a comma between two independent main clauses when there’s no coordinating conjunction. danach is an adverb, not a conjunction, so the two main clauses are simply separated by a comma:

Clause 1: Die provisorische Lösung funktioniert nur kurz,
Clause 2: danach nehmen wir den festen Plan. You could also write a period or semicolon instead. If you use und danach, then normally you don’t put a comma before und.

Is danach the same as nachdem?

No. danach is an adverb meaning “after that.” nachdem is a subordinating conjunction “after,” which introduces a subordinate clause with verb-final word order and usually perfect/pluperfect for past reference:

Danach nehmen wir den festen Plan.
Nachdem die provisorische Lösung nur kurz funktioniert hat, nehmen wir den festen Plan.

Why is it danach nehmen wir and not danach wir nehmen?

German main clauses are verb-second (V2). When an element like danach is put in first position, the finite verb must come second, and the subject follows:

Correct: Danach nehmen wir den festen Plan.
Incorrect: Danach wir nehmen …

Can I also say Wir nehmen danach den festen Plan? Any difference?

Yes, that’s correct too. Danach nehmen wir … puts emphasis on the time sequence by fronting danach. Wir nehmen danach … is more neutral in focus. Both are standard.

Why is it den festen Plan and not der feste Plan?

Because nehmen takes a direct object in the accusative. Plan is masculine: nominative der Plan, accusative den Plan. Hence den festen Plan.

Why does festen end in -en there?

Masculine accusative singular with a definite article (den) requires the adjective ending -en: den festen Plan. With no article, endings differ, but after a definite article in this slot, use -en.

Is den Plan nehmen idiomatic? Are there more natural alternatives?

It can be idiomatic in the sense of “to go with/choose the plan,” similar to choosing from options (like Ich nehme den Salat). If you mean “adopt/follow/implement” a plan, common alternatives are:

danach folgen wir dem festen Plan (follow the plan)
danach halten wir uns an den festen Plan (stick to the plan)
danach setzen wir den festen Plan um (implement the plan)
danach gehen wir zum festen Plan über or greifen auf den festen Plan zurück (switch/revert to the fixed plan) Choose based on the intended nuance.

What’s the difference between danach, dann, nachher, später, anschließend?

danach: “after that,” often referring back to what was just mentioned; slightly more formal/precise than dann in sequences with a clear “after.”
dann: “then,” general sequencer; very common and versatile.
nachher: “later/afterwards,” conversational; often near-future or informal.
später: “later,” more general and can be further in the future.
anschließend: “subsequently/afterwards,” more formal/written register.

In the sentence, danach fits well because it points to the time immediately after the short-lived solution.

Why present tense (nehmen wir) for a future action? Shouldn’t it be werden wir nehmen?

German often uses the present tense with a time adverbial to talk about the future. Danach nehmen wir … is perfectly normal. You can use werden for emphasis or clarity, but it’s not required: Danach werden wir den festen Plan nehmen is also correct, but not necessary.

Any pronunciation tips for Lösung, kurz, Plan?

Lösung: ö is like French “eu” in “deux,” a rounded front vowel; the s sounds like
kurz: short vowel [kʊrts]; final z is [ts].
Plan: long a [plaːn]. Nouns like Lösung and Plan are capitalized in German.