Hello friends, is it possible to animate equation with solidworks 2016?

You could try animating display states. Create multiple versions of the revolved body, each one using a different curve with a different k. You can then animate the visibility of each body, sequentially changing the visibility/transparency of each body one after the other, kind of like a time lapse video.

Hi Younsi

I made the global variable "k" = to a sketch dimension (just to make things easier).  Unfortunately (as usual) I couldn't get the Motion Study to work.

So I recorded a macro of editing the dimension, CTRL-Q rebuild and save as png

This gave me

Option Explicit

' ******************************************************************************
' C:\Users\369\AppData\Local\Temp\swx6468\Macro1.swb - macro recorded on 02/28/18 by 369
' ******************************************************************************
Dim swApp As Object

Dim Part As Object
Dim boolstatus As Boolean
Dim longstatus As Long, longwarnings As Long

Sub main()

Set swApp = _
Application.SldWorks

Set Part = swApp.ActiveDoc
boolstatus = Part.Extension.SelectByID2("D1@Sketch1@eqani.SLDPRT", "DIMENSION", 3.98313009457744E-02, 5.88555797084891E-02, 0.111978588735138, True, 0, Nothing, 0)
Dim myDimension As Object
Set myDimension = Part.Parameter("D1@Sketch1")
myDimension.SystemValue = 0.003
boolstatus = Part.ForceRebuild3(True)
Part.ClearSelection2 True
longstatus = Part.SaveAs3("C:\Users\369\Desktop\images\eqani.PNG", 0, 0)
End Sub

I then just edited the macro to create a loop

Option Explicit

' ******************************************************************************
' C:\Users\369\AppData\Local\Temp\swx6468\Macro1.swb - macro recorded on 02/28/18 by 369
' ******************************************************************************
Dim swApp As Object

Dim Part As Object
Dim boolstatus As Boolean
Dim longstatus As Long, longwarnings As Long

Sub main()

Set swApp = _
Application.SldWorks

Set Part = swApp.ActiveDoc
Dim myDimension As Object
Set myDimension = Part.Parameter("D1@Sketch1")
Dim k As Integer
Dim framecount As Integer
framecount = 0
For k = 1 To 300
    myDimension.SystemValue = k / 10000
    boolstatus = Part.ForceRebuild3(True)
    longstatus = Part.SaveAs3("C:\Users\369\Desktop\images\eqani" & framecount & ".PNG", 0, 0)
    framecount = framecount + 1
Next k
End Sub

Then just add the images to your favourite Move Maker and you're done