use reduction of order to solve the problem...
x''(t)-4x(t)=2. First find the homogeneous x''(t)-4x(t)=0, characteristic equation m^2-4=0, m1/2=+-2, xh=C1*e^(m1*t)+C2*e^(m2*t)=C1e^(2*t)+C2*e^(-2*t). As we see that a non homogeneous part in start equation is 2, xp must be constant. x=xh+xp. Substitute this in start equation (C1*e^2t+C2*e(-2t)+xp)''-4(C1*e^2t+C2*e(-2t)+xp)=2, xp''=0, -4xp=2, xp=-1/2.
derdack, yes, the problem can be solved that way, but I don't believe it is a god idea to advise a person to ignore the teacher's or text's instructions. Slapmaxwell1 says he was instructed to use "reduction of order". It is not at all uncommon to ask a person to solve a simple problem using a more complicated technique in order to practice that technique.
Slapmaxwell1, yes, letting reduces the left side of the equation to but you appear to have left out the right side of the equation. You have so that and, letting w= u', .
That is now a first order equation linear equation. It has as integrating factor:
You are right, but it is completly corect that we have other ways for solving which is important for learner. (John - Beautiful mind) .
True, but I was taught reduction of order before your method. The different methods come in their own itme.
Originally Posted by derdack
Yes. Both of us are right...
i am starting to see why you guys were so pissed that i wasnt using latex...I apologize. learning the commands in beginning is a bit troublesome and take a lil extra time, but its totally worth the effort.
ok ok i see it now.
if i let then
ok so so
there for so because i found Yc I would just put it all together for my final answer. thanks again!