AMATH250 Lecture Notes - Partial Fraction Decomposition, Linear Equation, Initial Condition
12 Apr 2013
School
Department
Course
Professor
Document Summary
De for unknown function t is independent variable y is dependent variable where when substitute into de, we get identities for and. Example: newton"s second law is force, may depend on. For vertical motion of small object of mass , known. State of motion in mechanics is given by and. What it sounds like: initial conditions that allow the general solution to the de to be fixed to a single result. In this situation we can introduce a new dependent variable for. For some (*) is an order differential equation. Coefficients are given functions of as is the term. For , this is a linear, non-homogeneous, order. General solution and are arbitrary constants and they make this a general solution. Look at the general solution and find and in general solution to accommodate the ic"s. Particular solution which satisfies both the original differential equation and the initial conditions. We solved an initial value problem (ivp) a de plus ic"s at.
