We investigate the asymptotic properties as t → ∞ of the following differential equation in the Hilbert space H: $\ddot x(t) + a(t)\dot x(t) + \nabla G(x(t)) = 0,t \ge 0,$ where the map \[\mathbb{R}_ ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

First‑order differential equations, linear and separable equations, integrating factors, applications. Second‑order linear differential equations. Fundamental solutions, linear independence, Wronskian ...