- #1

sdoyle1

- 23

- 0

## 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..