Trigger a button click with JavaScript on the Enter key in a text box

I have one text input and one button (see below). How can I use JavaScript to trigger the button's click event when the Enter key is pressed inside the text box?

There is already a different submit button on my current page, so I can't simply make the button a submit button. And, I only want the Enter key to click this specific button if it is pressed from within this one text box, nothing else.

<input type="text" id="txtSearch" />
<input type="button" id="btnSearch" value="Search" onclick="doSomething();" />

In jQuery, the following would work:

$("#id_of_textbox").keyup(function(event) {
    if (event.keyCode === 13) {
        $("#id_of_button").click();
    }
});

$("#pw").keyup(function(event) {
    if (event.keyCode === 13) {
        $("#myButton").click();
    }
});

$("#myButton").click(function() {
  alert("Button code executed.");
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

Username:<input id="username" type="text"><br>
Password:&nbsp;<input id="pw" type="password"><br>
<button id="myButton">Submit</button>

Or in plain JavaScript, the following would work:

document.getElementById("id_of_textbox")
    .addEventListener("keyup", function(event) {
    event.preventDefault();
    if (event.keyCode === 13) {
        document.getElementById("id_of_button").click();
    }
});

document.getElementById("pw")
    .addEventListener("keyup", function(event) {
    event.preventDefault();
    if (event.keyCode === 13) {
        document.getElementById("myButton").click();
    }
});

function buttonCode()
{
  alert("Button code executed.");
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

Username:<input id="username" type="text"><br>
Password:&nbsp;<input id="pw" type="password"><br>
<button id="myButton" onclick="buttonCode()">Submit</button>