Question

find wronskian without solving cos(t)y''+sin(t)y'-ty=0

Answer 1

I was thinking \[\cos(t)r ^{2}+\sin(t)r -t\]but I think you need to get that equation only in terms of r

Answer 2

I'm now thinking you need to solve it as a Y(h) free response problem

Answer 3

yeah try that cost m^2 + sint m-t=0
m1=[-sin t +sqrt(sin^2 t -4t cos t)]/2cos t
m2=[-sin t -sqrt(sin^2 t -4t cos t)]/2cos t or
m1=-(1/2)tam t +sqrt(sin^2 t -4t cos t)
m2=-(1/2)tan t -sqrt(sin^2 t -4t cos t)
W(e^-(1/2)tam t +sqrt(sin^2 t -4t cos t),e^-(1/2)tam t -sqrt(sin^2 t -4t cos t)
W=[e^m1 e^ m2]
[e^m1' e^m2'] you can do derivative of it

Answer 4

do the derivative of y1=e^-(1/2)tam t +sqrt(sin^2 t -4t cos t) and
y2=e^-(1/2)tam t -sqrt(sin^2 t -4t cos t)

Answer 5

the wroskian W=[y1 y2]
[y1' y2']