(d^2y/dx^2) + 7(dy/dx) +12y=0,
y(0)=1,
dy/dx(0)=3.
Find lim(x->infinity) y(x)
2007-10-21 00:56:09 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I'll tell you how to start.
The form of solution to this equation is well known. Think about what function is the same/related to its own derivative... that's right... the exponential. You have two initial conditions and therefore two parameters to play with:
y(x)=a*e^(b*r)
Take that and put it into the equation above. See where you can go from there.
2007-10-21 01:00:50 · answer #1 · answered by kain2396 3 · 0⤊ 0⤋
The auxilliary equation is u^2 + 7u + 12 = 0, with solutions u = -4 and u = -3. Therefore the general solution of the diff. eq. is y = Ae^(-4x) + Be^(-3x). You can find A and B by using the initial values. The limit as x -> inf is A + B.
2007-10-21 08:17:00 · answer #2 · answered by Tony 7 · 0⤊ 0⤋
The limit if x==> -infinity is - infinity and if x==> +infinity is 0
You have to calculate A and B
2007-10-21 10:01:27 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
y(x) will go to zero as x --> infinity NOT A+B
2007-10-21 08:48:05 · answer #4 · answered by cp_exit_105 4 · 0⤊ 0⤋