Initial value problems (IVPs) are mathematical problems that seek to determine a function based on its values at a specific point in time, alongside differential equations governing the system. IVPs are crucial in understanding the behavior of dynamical systems, as they establish conditions at the outset that guide the evolution of solutions over time. They play a significant role in methods like convolution and Duhamel's principle, which are used to solve linear non-homogeneous differential equations.
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