Learn Dutch: Wij hebben de pectine in het water opgelost. - We have dissolved the pectin in the water.

The verb oplossen (to dissolve) is a mutative verb, meaning it describes a change of state. When it is used transitively, meaning someone is actively causing the change to a direct object, it takes hebben. Because "we" are actively dissolving the direct object (de pectine), we use hebben. If the sentence were intransitive and the pectin was just dissolving on its own (e.g., "The pectin has dissolved in the water"), you would use zijn: De pectine is in het water opgelost.

Is opgelost a separable verb, and how is the past participle formed here?

Yes, the infinitive is oplossen (to dissolve). Because it is a separable verb, the ge- prefix of the past participle gets sandwiched between the separable prefix (op-) and the verb stem (lost), giving us op-ge-lost.

Why is the phrase in het water placed before the verb opgelost?

In Dutch main clauses in the perfect tense, the conjugated auxiliary verb (hebben) takes the second position, and the past participle (opgelost) is sent to the very end of the clause. Additional information like the prepositional phrase in het water naturally falls in the middle, before the final participle.

I've seen oplossen used to mean "to solve" a problem. Is it the exact same word?