Bitte bleib ruhig, wir finden eine Lösung.

Because this is a command addressed to one person in an informal way.

The full verb is bleiben = to stay / to remain.
For the informal du command, German usually uses the verb stem without -en:

• du bleibst = you stay
• Bleib! = Stay!

So Bitte bleib ruhig means Please stay calm.

Nothing is missing. In German, the informal imperative often leaves out du.

So instead of:

• Du bleib ruhig

German normally says:

• Bleib ruhig

If you want, you can add du for emphasis or emotion:

• Bleib du ruhig.

But in a normal sentence, leaving it out is standard.

Here ruhig means calm.

The adjective ruhig can mean different things depending on context, such as:

• calm
• quiet
• still

In Bitte bleib ruhig, it means stay calm, not just stay quiet.

Yes, bitte is flexible.

These are all natural:

• Bitte bleib ruhig.
• Bleib bitte ruhig.

Both mean Please stay calm.

Starting with bitte can sound a little softer or more immediately polite, but both versions are very common.

Because this sentence contains two main clauses:

1. Bitte bleib ruhig
2. wir finden eine Lösung

In German, main clauses placed next to each other are often separated by a comma, especially when the pause is natural and the meaning is clear.

It works like English:

• Please stay calm, we’ll find a solution.

German often uses the present tense to talk about the future when the meaning is clear from context.

So:

• wir finden eine Lösung

can mean:

• we find a solution
• we’ll find a solution

In this context, it clearly means we’ll find a solution.

German does have a future form:

• wir werden eine Lösung finden

But that is not necessary here. The present tense sounds very natural.

Eine Lösung means a solution, while die Lösung means the solution.

Using eine suggests:

• we do not yet know exactly what the solution is
• some solution will be found

So wir finden eine Lösung means we’ll find a solution.

If you said wir finden die Lösung, it would sound more like:

• we’ll find the solution
• there is one specific solution

Because Lösung is a noun, and in German all nouns are capitalized.

So:

• die Lösung = the solution
• eine Lösung = a solution

This is one of the most noticeable spelling rules in German.

This is normal German main clause word order:

• wir = subject
• finden = verb
• eine Lösung = object

So the pattern is:

• subject + verb + object

That is the standard order in simple statements.

It is informal because it uses the du imperative.

You would say this to:

• a friend
• a family member
• a child
• someone you address with du

The formal version would be:

• Bitte bleiben Sie ruhig.

That is what you would say to someone you address with Sie.

A rough pronunciation guide:

• bleib sounds a bit like blype, with the German ei sounding like English eye
• ruhig is roughly ROO-ig or ROO-ikh, depending on accent

A few details:

• ei in bleib = like eye
• ru- in ruhig has a long oo sound
• the final sound in ruhig can be pronounced differently in different regions

For a learner, ROO-ig is a good starting approximation.

Not usually. In this sentence, the natural meaning is Please stay calm.

If you wanted to say Please be quiet, German would more naturally use:

• Bitte sei ruhig.
• Bitte seid ruhig.
• Bitte seien Sie ruhig.

Even though ruhig can relate to quietness, with bleib ruhig the emotional meaning stay calm is the most likely one.

Yes, but it sounds a bit more formal, old-fashioned, or emphatic.

For the du imperative, many verbs allow a shorter form and sometimes a longer form:

• bleib ruhig
• bleibe ruhig

In everyday spoken German, bleib ruhig is much more common.

So for normal conversation, Bitte bleib ruhig is the best choice here.