Question

Why does the wronskian always = 0 or never =0 if
y=c1y1+c2y2, if y1 and y2 are particular solutions(their wronskin)
where y is the general solution to y''+ay'+by+c=0

Answer 1

hi

Answer 2

@ganeshie8

Answer 3

hey when is the always 0 case seen again

Answer 4

0 is easy to see as when the solutions are dependent we can write y1 = 2y1
and so the determinant is always 0

Answer 5

yes i saw that but does this stuff also cover when its not possible case

Answer 6

i think ts bit hard to prove the non 0 case - how do u prove an abstract function is never 0... hmm

Answer 7

@nipunmalhotra93

Answer 8

that i was gonna pull outta

Answer 9

matrix proofs that a invertible matrix cannot have 0 determinant

Answer 10

still working on it

Answer 11

thats valid if the matrix elements are ordinary numbers...

proving its never 0, and it cannot have 0 determinant - both are same... we cannot use one for proving the other

Answer 12

oh

Answer 13

cant i make the argument that they are numbers since we are subbing in the values of x, to see when y1 and y2 evaluated at a point Xo
if i was given the initial condition
y(Xo)=A
y'(Xo)=B