Solve two equations with Modified bessel functions?

Questions
,
1

Hi

I am trying to solve two equations with bessel functions in them,

C1*BesselK[0, 3.7268e4*x] =1.3e-6 

x = 53.66*C1*BesselK[1, 3.7268e4*x]

here x and C1 are unknown constants. I have tried to solve it with the following expression, but to no use.

Solve C1*BesselK[0, 3.7268e4*x] =1.3e-6

and

x = 53.66*C1*BesselK[1, 3.7268e4*x]

Any suggestions are more than welcome. Regards

2

Without knowing C1 it is not possible, BesselK is a power series: You can give values to C1, solve numerically and create an interpolation table between C1 and the solution. Keep in mind, Mathematica has a syntax which it not the one of F77 or C89.

In[10]:= With[{C1 = 3.},
 FindRoot[53.66*C1*BesselK[1, 3.7268 10^4 x] - x, {x, 0.0000001, 0.1}]
 ]
Out[10]= {x -> 0.000325222}

In[13]:= (53.66*3.*BesselK[1, 3.7268 10^4 x] - x) /. %10
Out[13]= 1.59181*10^-14

In[11]:= With[{C1 = 3.},
 FindRoot[C1*BesselK[0, 3.7268 10^4 x] - 1.3 10^(-6), {x, 0.0000001, 0.1}]
 ]
Out[11]= {x -> 0.000363983}

In[12]:= 3. BesselK[0, 3.7268 10^4 x] /. %11
Out[12]= 1.3*10^-6