Mathematical description of differential equation solving electrical circuits

We show that the working principle of the differential equation solving analog electrical circuits is exactly the same as the Picard's method available for numerically solving the ordinary differential equations. The integrator circuit (low-pass filter) uses an initial condition and electrical input signal to generate the Maclaurin's series of a time varying function in recursion. This direct connection between the differential equation solving electrical circuits and Picard's method can be exploited to simplify the procedure of Picard's method to solve any order linear and nonlinear differential equations.