It should be an easy task unless there are more conditions.
You may code like -
C# Approach
On dropdownlist SelectedIndexChanged
(Make sure that you have set property AutoPostBack="True" for that dropdownlist)
If(drp.SelectedValue=="first")
{
txt1.Visible=false;
txt2.Visible=true;
}
else if(drp.SelectedValue=="second")
{
txt2.Visible=false;
txt1.Visible=true;
}
Javascript Approach
aspx snippet
<asp:DropDownList ID="drp" runat="server" onchange="HideTextBoxes();"
Javascript snippet
<script>
function HideTextBoxes()
{
var selectedvalue= document.getElementById("<%=drp.ClientID%>").value;
if(selectedvalue == "first")
{
document.getElementById("<%=txt1.ClientID%>").style.display = 'none';
document.getElementById("<%=txt2.ClientID%>").style.display = '';
}
else if(selectedvalue == "second")
{
document.getElementById("<%=txt2.ClientID%>").style.display = 'none';
document.getElementById("<%=txt1.ClientID%>").style.display = '';
}
}
</script>