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if I plug in the headphones jack, the radio does not recognize that it has headphones, and after I remove them, the phone stays in the headphones mode and needs to be restarted to go back to the speaker
Hi @Machociprian,
I'm sorry to hear this. 
Have you tried with more then one pair of earphones to make sure they are not causing this behavior? You can also restart your device to safe mode to see if this behaviour may be caused by one of your downloaded apps as these will be temporarily disabled in this mode.
If there is no change, I recommend that you perform a software repair using Xperia Companion.
Let me know how it goes. 
I tried.....many earphones,safe mode....but nothing.Just with restart and Sound About but its inadmisibile to make this everytime i use earphone.....
The phone must recognize when i put or take the jack....