The most straightforward way to do this declaratively is to set up one page for the New and Edit action for the object,  and set up another for the Display (detail) view.  Your field would only be on the New/Edit page. 

You could force users to use the edit page by makeing the Display page read only - and including a “Edit” redirect button. 

No Actually i have to use it for the related list of the tasks.So all this are in the same page.And in related list of task there we are having quick task create in table. So there when ever i do the table actions of Insert or Update any tasks then it should display the text field and else in details it should not show. How i can achieve it? Thanks

Ok Got it. 

In your related table -  select the row action and change the action to “Pop up”.   Here you can have the text box displayed (along with any other data you are interested in - as long as it is in your model). 

Turn off the standard “Allow Inline Record Creation”  -  which will remove the little green circle.   But add a Feature of type “Global Action”.  The Type for this action should also be popup.   When you configure this popup it shoudl connect to a different model “New Task”  that has Advanced properties “Create Default Row if Model has None” - selected and “Load Model on Page Load” - NOT selected.   Configure this popup to collect all your data - including the text box.