David Shulman
New member
- Joined
- Jul 29, 2020
- Messages
- 2
Hello,
I have a heterogeneous modified Bessel equation:
[MATH]z'' +\frac{1}{r}z'-\frac{1}{v^2}z=G(r),[/MATH]and I interesting in the solution of the function on extremum points,
[MATH]z'(0)=0[/MATH]so I solve the equation:
[MATH]z''-v^2z=G(r),[/MATH]I have for homogeneous solution:
[MATH]z_h=c_1 exp(v^{-1} r)+c_2 exp(-v^{-1} r) [/MATH]and for a Particular solution with Variation of Parameters:
[MATH]z_p=exp(v^{-1} r)∫G(r)/(2v^{-1}) exp(-v^{-1} r)+exp(-v^{-1} r)∫G(r)/(2v^{-1} ) exp(v^{-1} r)[/MATH]But how I can find the constant parameters in homogeneous solution? Probably I can not use my boundary condition, because I change my function...
I have a heterogeneous modified Bessel equation:
[MATH]z'' +\frac{1}{r}z'-\frac{1}{v^2}z=G(r),[/MATH]and I interesting in the solution of the function on extremum points,
[MATH]z'(0)=0[/MATH]so I solve the equation:
[MATH]z''-v^2z=G(r),[/MATH]I have for homogeneous solution:
[MATH]z_h=c_1 exp(v^{-1} r)+c_2 exp(-v^{-1} r) [/MATH]and for a Particular solution with Variation of Parameters:
[MATH]z_p=exp(v^{-1} r)∫G(r)/(2v^{-1}) exp(-v^{-1} r)+exp(-v^{-1} r)∫G(r)/(2v^{-1} ) exp(v^{-1} r)[/MATH]But how I can find the constant parameters in homogeneous solution? Probably I can not use my boundary condition, because I change my function...
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