Solution of 2nd Order O.D.E Name Institution Solution of 2nd Order O.D.E Introduction The general linear differential equation of order n is an equation that can be written in the form (1) Where … ; where are functions of only or constants and is a function of only. It is important to note that if then the equation (1) is said to be linear and homogenous which indicates that all the terms are of the same 1st degree inand its derivatives. Also if then equation (1) is called the method of variation of parameters. Method of inverse D – operator method This method is also referred to as the short cut method because it generally applies inverse D – operation on the R.H.S and consequently provides the solution to the problem. From equation (2) we have and when finding the particular solutions we let Sometimes the method is not effective when the function on the R.H.S is too complicated and therefore the method which is most powerful is the method of variation of parameters. [...]
In a 2 page essay, analyze when it is best to use undetermined coefficients, versus variation of parameters, or other methods, for equations of type y'' + a y' + b y = f(t), where y=y(t).