{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":6,"macros":1,"defined_names":13,"comments":1},"read":"whole","date_system":"1900"}

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[null,"            Picards Method"]
[null,"  for the Differential Equation"]
[null,null,"       y' = f(x, y)"]
[]
[null,"  This DIGMath graphing utility illustrates "]
[null,"Picard's Method to approximate the solution   "]
[null,"    of any first order differential equation"]
[null,null,"          y' = f(x, y)"]
[null,"        with initial conditions x0 and y0"]
[null,"        extending from x = a  to x = b."]
[]
["Enter the function in terms of both x and y:"]
[{"$nulls":4},"f( x, y) =","y"]
[]
["Now enter the initial conditions:"]
[null,"The initial value x0 of  x is",null,null,0,{"$nulls":3},"Now select which Picard approximations you want to see  "]
[null,"The initial value y0 of  y is",null,null,1]
[{"$nulls":9},true]
["To what value of x should the solutions extend?"]
[null,null,"b = xMax =",2,{"$nulls":5},true]
[]
[{"$nulls":9},true]
[]
[]
[{"$nulls":9},false]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2",{"$nulls":7},false]
[null,"   Item 3"]
[null,"   Item 4",{"$nulls":7},false]
[]
[]
["To access/download all the DIGMath Apps for Differential Equations"]
["     Click this link:",null,"https://we-dig-math.org/dynamic-differential-equations.html"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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