MAT 2384 Lecture Notes - System Of Linear Equations, Bernoulli'S Principle, Integrating Factor
17 Sep 2013
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Document Summary
A di erential equation is an equation involving an unknown function and some of its derivatives. Here y is really y(t). it"s easy to spot which are the variables and which are the unknown constants: variables have derivatives. A derivative is a rate of change, so functions are used because they change (with respect to time, or space or whatever). The order of the di erential equation is the order of the highest derivative appearing in the equation. 0. 1. 4 examples has order 1 while has order 2. = 10y2 + sin(t) dy dt y00 + 10y0y = 0. A linear equation is an equation in which the unknown function y(t) and its derivatives appear by themselves. + sin(t) d2y dt2 = 10 dt is nonlinear while is linear. y00 + 10y0 + 2y = 0. An existence theorem might tell us if it does. Some equations may have no solutions at all and some may have in nitely many.
