I have a test coming up involving variation of parameters and I am practicing. I got stuck on this one, I know it should just be algebra but now I'm lost.
Using the system of equations:
U1'(y1)+U2'(y2) = 0
U1'(y1')+U2'(y2') = f(x)
I need to solve for U1' and U2'.
I started with y" + 16y = 4Tan(4t)
I found that r = 0 (+-) 4i, and y(c) = Cos(4t) + Sin(4t)
using that fact I did what was necessary to enter that into the system of equations and now I can't figure out what I need to do in order to remove U1' and U2' from the equation separately in order to figure out what U2' and U1' are.
Any suggestions of what I should do next? What to multiply/divide/subtract/add/etc.
Should I have split up the Cos(4t) and Sin(4t) so that y1= Cos(4t), and y2 = Sin(4t)?