- #1

karlmartin

- 11

- 0

This is the equation under discussion:

y'' - 2y' - 3y = x + 2

I'm asked to use the method of variation of parameters to determine a solution for this differential equation, but I reach a point where my the equations just look too ridiculous to continue.

The point I have in mind is where I finally get the second equation for the system of equations that is supposed to give me meaningful functions for the derivatives of the two variable functions.

These are my equations(the variable functions are u

_{1}and u

_{2}):

u

_{1}'e

^{3x}+ u

_{2}'e

^{-x}= 0

3u

_{1}'e

^{3x}- u

_{2}'e

^{-x}= x + 2

From these I am unable to extract equations for the variables that I would be able to integrate without resorting to some sort of external aid. Also, it seems unlikely that these overly difficult equations would really have be the result of the necessary work, considering this is from a beginner calculus course(Early Transcendentals, 6th international edition, chapter 17.3, problem 20).

I need to master this technique, but every problem I try ends up with me looking at an insane integral, puzzled beyond the twilight zone. Could someone please point out my mistake, or at least confirm that the equations are indeed correct and perhaps point out a method of simplification that doesn't result in an integral too hard to process?

Thank you very much for your time.