Question

If the wronskian = 0 of a differential equation, does this mean that the equation is linearly dependent?

Answer 1

Quoting from wikipedia:

The Wronskian can be used to determine whether a set of differentiable functions is linearly independent on an interval. This is useful in many situations. For example, if we wish to verify that two solutions of a second-order differential equation are independent, we may use the Wronskian. Note that if the Wronskian is zero everywhere in the interval, the functions may or may not be linearly independent. A common misconception is that W = 0 everywhere implies linear dependence; the third example below shows that this is not true. However, if all of f1, ..., fn are analytic, then W = 0 everywhere implies linear dependence.

Answer 2

wikipedia...lol

Answer 3

whats it mean by analytic O.o

Answer 4

http://en.wikipedia.org/wiki/Analytic_function

Answer 5

have the derivatives in all points...in the interval

Answer 6

what about in the case of x|x| where it is linearly independent but w = 0

Answer 7

y1= x^2 and y2= x|x|

Answer 8

o wait nvm d/dx |x| at 0 doesnt exist