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Solve this mixed partial differential equation

Posted 5 months ago
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This is my QS: enter image description here This is my Code:

4 Replies

enter image description here So you have the system and is underdetermined. That means the indicated function does not include enough equations to specify a solution.

Posted 5 months ago

Thanks

Posted 5 months ago

I add more equation as:

enter image description here

This is my code

It is still not solvable.

I tried with DSolve and NDSolve, but Mathematica fails.

With Maple 2020 I have: enter image description here

Translating to Mathematica code:

    ClearAll["`*"]
    sol = {R[z] -> R0*Exp[((Log[U0/UL] + 2*I*Pi*n)*z)/(2 L)], 
      u[z] -> U0/
       Exp[((Log[U0/UL] + 2*I*Pi*n)*z)/(2 L)]^2};(*  n\[Element]Integers *)

   u[z] /. sol[[2]] /. 
    z -> 0(*The equation satisfy a initial condition u[0]=U0 *)

    (* U0 *)

    {sol[[1]] /. n -> 0, sol[[2]] /. n -> 0}(*for n=0*)

    (* {R[z] -> R0 (U0/UL)^(z/(2 L)), u[z] -> U0 (U0/UL)^(-(z/L))} *)
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