### First-Order Differential Equations Review

First-Order Differential Equations Review We consider first-order differential equations of the form: ( ) ( ) ( ) 1 x t f t dt dx t + = τ (1) where f(t) is the forcing function. In general, the differential equation has two solutions: 1. complementary (or natural or homogeneous) solution, xC(t) (when f(t) = 0), and 2.