Question

Differential Equations QUIZ

Answer 1

a bessel equation

\[y'' + \frac{ 1 }{ x }y' + \left( 1-\frac{ n^{2} }{ x^{2} } \right)y = 0\]
. Use the transformation y = v x^(-0.5) and prove that the Bessel Differential Equations can be transformed into
\[v'' + \left( 1-\frac{ 4n^{2}-1 }{ 4x^{2} } \right)v = 0\]

My Questions is:
When compared with the equation of
\[u'' + u = 0\]
which has the solution u= sin x, to Bessel differential equations above and to the condition of n=0, at least there is a how to order solutions zero-order Bessel equation of the differensial (n = 0) in between intervals of \(\pi\) along the positive x axis

Answer 2

i mean.,
how much is the solution zero-order of the Bessel equations above at (n=0) in between intervals of \(\pi\) along the positive x axis

Answer 3

is u doing microwave engineering subject?

Answer 4

i'm doing on Math Methods for physicist :)

Answer 5

oh me see bessel eq's in antenna subject and it has no proof just result

Answer 6

yes.., i see :)., can u help me for this?

Answer 7

try:)actually engineering mathematics is different then general mathematics

Answer 8

ok.., :)

Answer 9

"how much the solution zero-order of the Bessel equations above at (n=0) in between intervals of π along the positive x axis"