You will have to use jQuery script provided by Bootstrap to achieve what you want —

<p>                    ---->>Updated here
<button type="button" class="btn btn-primary" id="rp_yes">Yes</button>
   <button type="button" class="btn btn-primary" id="rp_no">No</button>
</p>

Script

$('#rp_yes').click(function(){
            $("#password_reset_form").collapse('show');
                 $("#not_rem_p").collapse('hide');
        });
        $('#rp_no').click(function(){
                $("#not_rem_p").collapse('show');
                $("#password_reset_form").collapse('hide');
        });

$(<selector>).collapse('options') is the required change here. More documentations here Bootstrap Collapse

This should work.