# Differential equations

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Display solutions of the ordinary differential equation

$\displaystyle{ y'= f(t,y) }$

with initial value $\displaystyle{ (t_0,y_0) }$.

It is easy to incorporate sliders: give the slider a (unique) name and use this name in the equation. In the example below, the slider name is $\displaystyle{ c }$.

f(t,y)=

### The underlying JavaScript code

<form>
f(t,y)=<input type="text" id="odeinput" value="(2-t)*y + c"><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 slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});
var P = brd.create('point',[0,1], {name:'(t_0, y_0)'});
var f;

function doIt() {
var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 't, y');
f = function (t, yy) {
return [snip(t, yy[0])];
}
brd.update();
}

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

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