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Differential Equations QUIZ

Mathematics
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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
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
is u doing microwave engineering subject?

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Other answers:

i'm doing on Math Methods for physicist :)
oh me see bessel eq's in antenna subject and it has no proof just result
yes.., i see :)., can u help me for this?
try:)actually engineering mathematics is different then general mathematics
ok.., :)
"how much the solution zero-order of the Bessel equations above at (n=0) in between intervals of π along the positive x axis"

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