It is possible to solve a large class of ODEs by means of analog computers. Each of the pieces of the differential equation corresponds to an electronic component and if you wire them up the right way you get a circuit described by the ODE. <a href="http://en.wikipedia.org/wiki/Analog_computer">Wikipedia</a> has lots of information on the subject and a link like <a href="http://www.analogmuseum.org/library/handson.pdf">this</a> one gives explicit examples of circuits. It's not hard to build circuits for things like the <a href="http://en.wikipedia.org/wiki/Lorenz_attractor">Lorenz equation</a> and see a nice Lorenz attractors on an <a href="http://www.youtube.com/watch?v=6HWfdRZo1I4">oscilloscope display</a>.