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Find the solution y(x) to the initial value problem

(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 00:12:02 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

characteristic equation
r^2+7r+12=0 so r = ((-7+-sqrt(49-48))/2
so r= -4 and r=-3
y= a e^-4x+be^-3x
y´=-4ae^-4x -3be^-3x
At x=0
a+b=1
-4a-3b=3 b=1-a so -4a+3a-3=3 so a= -6 and b=7
y = -6e^-4x+7e^-3x
lim y x==> +infinity is 0
lim y x==> - infinity = lim 7e^-3x( -6/7*e^-x+1)
The first factor==>+infinity and the second to -infinity so the limit is -infinity

2007-10-21 02:06:01 · answer #1 · answered by santmann2002 7 · 0 0

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