MATH 1005 Study Guide - Comprehensive Final Exam Guide - Trigonometric Functions, Square Root, Ordinary Differential Equation
20 Nov 2018
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A differential equation (de) contains an unknown function (y = f(x)), derivatives of it and. Example: y" = cos x + 2, y""+ 2x = ex , xy"" + y" = x2. When the unknown function us a function of a single variable only, like y = f(x), the derivatives are (cid:862)ordinary(cid:863), ie y" = (cid:3052)(cid:3051) , and we have ordinary differential equation (ode) (pde). (cid:3052)(cid:3051), (cid:3052) If the unknown function depends on more than one variable, ie. u = f(x,y), we have partial derivatives. Order of a de is the order of the highest-ordered derivative that appears in it. The solution of a de is the unknown function y that satisfy it. Eg. y" = 2 + cos x y = 2x + sin x + c (general solution) To get a particular or unique solution, we need to add an initial condition (ic),
