Differential analyzer

Built by Vannevar Bush and Harold Hazen at MIT in 1928–1931, the differential analyzer is a general-purpose analog ODE solver. The core component is a wheel-and-disk integrator: a disk rotates at rate proportional to one variable; a wheel resting on the disk at a radial position proportional to a second variable rotates at their product — implementing ∫ y dx mechanically. Multiple integrators are chained via shafts and differential gears to represent higher-order ODEs. A torque amplifier (Bush's key innovation) prevents the tiny friction coupling from loading the computation. The MIT machine solved sixth-order ODEs; later machines solved 18th-order equations. The device is the missing link between the planimeter (single integral) and the fire-control computer (hardwired ODE). Speed: minutes per ODE solution (shaft rotation time). Capacity: up to 18th-order ODEs (later machines); ~3 significant figures.