gehorchen
to obey
To follow an order, instruction, or person and do what is required. The verb is typically used with the dative.
Der Hund gehorcht seinem Herrchen aufs Wort.
The dog obeys his owner instantly.

to obey
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to obey
To follow an order, instruction, or person and do what is required. The verb is typically used with the dative.
Der Hund gehorcht seinem Herrchen aufs Wort.
The dog obeys his owner instantly.

The verb 'gehorchen' (to obey) always requires the dative. The person or thing that one obeys is in the dative, not the accusative. A common mistake is using the accusative.
Die Kinder müssen ihren Eltern gehorchen.
The children must obey their parents.
'Gehorchen' (to obey) is an inseparable verb. The prefix 'ge-' remains firmly attached to the verb in all sentence forms and tenses and is never separated.
Er hat mir noch nie gehorcht.
He has never obeyed me.
The word 'gehorchen' (to obey) is related to 'horchen' (to listen attentively). So it means to 'listen' to an order and then carry it out.
Ein gut trainierter Hund gehorcht auf kleinste Signale.
A well-trained dog obeys the smallest signals.
In the figurative meaning, the subject is often a body part or a device that no longer works as desired. This use is often found in negative sentences.
Meine Stimme will mir heute einfach nicht gehorchen.
My voice simply won't obey me today.
to follow
'folgen' and 'gehorchen' can both mean doing what is required. But 'folgen' is broader and often more neutral: you can follow a piece of advice, a rule, or an instruction. 'gehorchen' sounds more strongly connected to duty, commands, and authority. It is often used when a person or animal does what someone with authority says. Learners may confuse the words because both can be used with the dative. Still, 'dem Rat folgen' (to follow the advice) sounds more natural than 'dem Rat gehorchen', while 'dem Lehrer gehorchen' (to obey the teacher) sounds more strongly like obedience.

Das Kind gehorcht der Lehrerin, weil sie klare Anweisungen gibt.
The child obeys the teacher because she gives clear instructions.
Bei der Arbeit folgt das Team den neuen Regeln für den Kurs.
At work, the team follows the new rules for the course.