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Emden-Fowler Differential Equation
I input into MAPLE the following differential eq & it returned that it is classified as an Emden-Fowler Differential Equation:
r^2*F"+1/r*F'-k^2*F=0 where F is a function of r
MAPLE was able to generate a solution. I am attempting to figure out how this eq is actually solved & I typed in Emden-Fowler into the SEARCH window on this website & got ZERO results.
Anyone know of some good resources that shows the method of solving this diff eq? If I am correct this equation is the result of separation of variables for solving the LaPlacian of displacement in the logitudinal direction for shear being applied to an annulus on the interior diameter surface in the longitudinal direction.
Keep in mind I am an engineer so some source that is too intensive in mathematical notation may not be that helpful.
my email: jberg3@unl.edu
I dont think that the
I dont think that the differential equation you posted can be obtained from the Laplace equation. For consistency, each term in the equation should have the units of (F/r^2), which is true for the second and third terms (where I am assuming that k is some wavenumber with units of 1/r).However, the first term has the dimensions of F, which is inconsistent. You might want to check your derivation.
i think
If i am right, the correct format should be 1/r^2*F"+1/r*F'-k^2*F=0
actually , the above function is zero order bessel function with the variable is ikr ,where i^2=-1. the analytical solution is J0(ikr) or H0(ikr)
LG
sorry
i made a typing error. The n order bessel function is F''+1/x*F'+(1-n^2/x^2)*F=0, the general solution is Jn(x) or Hn(x).
if you set n=0, x=ikr, where i^2=-1. the function change to be F"+1/r*F'-k^2*F=0, so the general soluion is J0(ikr) or H0(ikr).