And for number 5), the variation of parameters methode is the methode taht using wronskian ? Sorry i can't remember the name of the methods...
First I suggest you read the following article:After I get the homogeneous solution then wath should I do, I mean, how to use the undetermined coefficient method? should I convert the "sinx " in to "e^ia thing
Method of undetermined coefficients - Wikipedia, the free encyclopedia
after reading this article you'll come to the conclusion that you should assume a particular solution of following form:
just plug it in the ode and equate the appropriate coefficients.