You need to test for the negation of the Regular Expressions because you want the validation to alert upon failure,
(is_valid = !/^[0-9]+$/.test(x))
Example :-
<form action="" method="POST" name="cdp_form" id="cdp_form">
<input type="text" id="phone_number" name="phone_number" placeholder="Enter your phone number" maxlength="10" onkeyup="validateForm()">
<button type="submit" name="SEND" class="btn btn-brown">Send</button>
</form>
<?php echo $successmsg; ?>
<script>
//form validation
function validateForm()
{
var x=document.forms["cdp_form"]["phone_number"].value
if (x==null || x=="")
{
alert("Phone number field must be filled in");
cdp_form.phone_number.focus();
return false;
}
else if (is_valid = !/^[0-9]+$/.test(x))
{
alert("Phone number field must have numeric characters");
cdp_form.phone_number.focus();
return false;
}
}
</script>