- #1
sdoyle1
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Homework Statement
y1(t) and y2(t), 2 solutions of the equation:
y'' +ay'+by=0, with a,b εℝ - {0}
a) Determine:
d/dt w(y1,y2)
where w(y1,y2) is the wronskian of y1(t) and y2(t)
b)
Deduce that if (y1(0),y1'(0)^T and (y2(0), y2'(0))^T are 2 linearly independent vectors. Then y1(t) and y2(t) are linearly independent functions.
Homework Equations
^T = transpose
the wronskian is the det |y1 y2|
|y1' y2'| = y1y2' -y2y1'
Vectors are linearly independent if w(y1,y2) does not equal 0
The Attempt at a Solution
For part a, do I just find the wronskian of y1 and y2 and then take the derivative?
For part b I'm super confused. I notice that if you transpose the two vectors and put them into a determinant than they are the wronskian.. other than that I'm pretty lost..