Updating an input's value without losing cursor position

I want to mandate that the value of a text box is lowercase using JavaScript. I've tried the code below, but the cursor jumps to the end of the input every time you press a key. How can I avoid this?

$("#beLowerCase").keyup(function(){
    $(this).val( $(this).val().toLowerCase() );
});

$("#beLowerCase").on('input', function(){

    // store current positions in variables
    var start = this.selectionStart,
        end = this.selectionEnd;
    
    this.value = this.value.toLowerCase();

    // restore from variables...
    this.setSelectionRange(start, end);
});

(fiddle)

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This actually works with CSS as well:

#beLowerCase{
  text-transform:lowercase;
}

And server can take care of the actual lower-casing...