Researches on solution of differential equations using mechanical devices started (discounting planimeters) at least as early as 1836, when the french physicist Gaspard-Gustave Coriolis designed a mechanical device to integrate differential equations of the first order. The analyzer was invented in 1876 by James Thomson, brother of Lord Kelvin. Mechanical integrators for differential equations were also designed by the Italian mathematician Ernesto Pascal in 1913.

A practical version of Thomson's differential analyzer was first constructed by H. W. Nieman and Vannevar Bush starting in 1927 at MIT. They published a full report on the device in 1931. D. R. Hartree of Manchester University brought the design to England, where he constructed his first model (with his student, Arthur Porter) in 1934.

In the United States, differential analyzers were built at Wright-Patterson Air Force Base and in the basement the Moore School of Electrical Engineering at the University of Pennsylvania in the early 1940s; the latter was used extensively in the assembly of artillery firing tables prior to the invention of the ENIAC, which, in many ways, was modeled after the differential analyzer.

The differential analyzer was used in the development of the bouncing bomb, used to attack German hydroelectric dams during World War II. Differential analyzers have also been used in the calculation of soil erosion by river control authorities. It was eventually rendered obsolete by electronic analog computers and later digital computers.

The differential analyzer as pictured above is one of the few built with FAC parts, back in the late 1950's.