// Numbas version: exam_results_page_options
{"name": "Solution curves and  Vector fields 3: $dy/dx=x^3-y^3$", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a"], "rulesets": {}, "variables": {"a": {"description": "<p>Just a filler - not used. Need a variable to publish.</p>", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "1"}}, "extensions": ["jsxgraph"], "functions": {"testfield": {"type": "html", "definition": "\n      var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-5,5,5,-5],grid:true,axis:true});\n        function f(x,y){return x*x*x-y*y*y;}\n      var str = \"x*x*x-y*y*y\";\n        var board = div.board;\n        for(var i=-10;i<10;i++){\n      for(var j=-10;j<10;j++){\n       //board.create('point',[i/2,j/2],{size:2,name:'',face:'+'});\n        var len=4;\n      // the length of a segment is 1/4\n       var d=1/(len*(Math.pow(1+Math.pow(f(i/2,j/2),2),0.5)));\n         board.create('segment',[[i/2,j/2],[i/2+d,d*f(i/2,j/2)+j/2]]);}\n        }\n      //var N = board.create('slider',[[-4,4],[4,4],[-5,2.5,5]], {name:'N'});\n      var P = board.create('point',[0,0], {name:'(x_0,y_0)'});\n       \n      function doIt() {\n        var txt = JXG.GeonextParser.geonext2JS(str);\n        f = new Function(\"x\", \"yy\", \"var y = yy[0]; var z = \" + txt + \"; return [z]\");\n        board.update();\n      }\n       \n      function ode() {\n         return JXG.Math.Numerics.rungeKutta('heun', [P.Y()], [P.X(), 5], 200, f);\n      }\n      function ode1() {\n         return JXG.Math.Numerics.rungeKutta('heun', [P.Y()], [P.X(), -5], 200, f);\n      } \n      var g = board.create('curve', [[0],[0]], {strokeColor:'red', strokeWidth:2});\n      g.updateDataArray = function() {\n      var data = ode();\n      var data1= ode1();\n      var h = (5-P.X())/200;\n      var h1 = (5+P.X())/200;\n      this.dataX = [];\n      this.dataY = [];\n      for(var i=0; i<data1.length; i++) {\n      this.dataX[i] = -5+i*h1;\n      this.dataY[i] = data1[data1.length-i-1][0];\n      }\n      for(var i=data1.length; i<data1.length+data.length; i++) {\n      this.dataX[i] = P.X()+(i-data1.length)*h;\n      this.dataY[i] = data[i-data1.length][0];\n      }\n      };\n      doIt();\n        return div;\n      \n      \n        \n      \n        ", "language": "javascript", "parameters": []}}, "variable_groups": [], "metadata": {"description": "<p>Using Jsxgraph to draw the vector field for a differential equation of the form $\\frac{dy}{dx}=f(x,y)=x^3-y^3$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.</p>\n<p>If you want to modify $f(x,y)$ simply change the definition of &nbsp;$f(x,y)$ and that of the variable &nbsp;str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>{testfield()}</p>\n<p></p>", "name": "Solution curves and  Vector fields 3: $dy/dx=x^3-y^3$", "parts": [{"type": "information", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "prompt": "<p>Vector field for the differential equation \\[\\frac{dy}{dx}=f(x,y)=x^3-y^3\\]</p>\n<p>You change the function $f(x,y)$ by modifying the function $f(x,y)$ in the testfield function defined in Extensions and scripts.</p>\n<p>You have to use Javascript notation for powers and standard functions when you define $f(x,y)$ in testfield.</p>\n<p>If you want to see the solution curve through a particular point then drag the point labeled $(x_0,y_0)$ to it.&nbsp;</p>", "marks": 0}], "tags": [], "advice": "<p>Move the point $(x_0,y_0)$ to see the solutions through that point.</p>", "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}