# Differential equations

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Display solutions of the ordinary differential equation

$x'= f(t,x)$

with initial value $(x_0,y_0)$.

f(t,x)=

### The underlying JavaScript code

<form>
f(t,x)=<input type="text" id="odeinput" value="(2-t)*x"><input type=button value="ok" onclick="doIt()">
</form>
var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
var P = brd.create('point',[0,1], {name:'(x_0,y_0)'});

function doIt() {
var t = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
f = new Function("t", "xx", "var x = xx[0]; var y = " + t + "; return [y]");
brd.update();
}

function ode() {
return JXG.Math.Numerics.rungeKutta(JXG.Math.Numerics.predefinedButcher.Heun, [P.Y()], [P.X(), P.X()+N.Value()], 200, f);
}

var g = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'});
g.updateDataArray = function() {
var data = ode();
var h = N.Value()/200;
this.dataX = [];
this.dataY = [];
for(var i=0; i<data.length; i++) {
this.dataX[i] = P.X()+i*h;
this.dataY[i] = data[i][0];
}
};
doIt();