Differential Equations and The - Braun, Martin 7579 · Problem 2.12.Ex1

Introduction to Applied Nonlinear Dynamical Systems and Chaos — Braun, Martin 7579

Mathematics — Calculus · ode-general-solution-repeated-root

Problem

Let aa be a fixed constant. Show that every solution of the differential equation (d2y/dt2)+2a(dy/dt)+a2y=0(d^2y/dt^2)+2a(dy/dt)+a^2y=0 can be written in the form y(t)=[c1+c2(t−a)]e−a(t−a).y(t)=[c_1+c_2(t-a)]e^{-a(t-a)}.

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