Power series solution to a differential equation











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If $f(rho)$ satisfies $frac{df}{drho}=frac{f(2rho)}{2f(rho)}$, I am trying to derive the form of $f(rho)$ by using a power series expansion $f(rho)=sum a_n rho^n$ and show that $f(rho)$ can be $rho$, $Rsin(rho/R)$ or $Rsinh(rho/R)$. I am getting stuck.



What should be further steps?



Thanks for the help in advance.






differential-equations power-series







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    If $f(rho)$ satisfies $frac{df}{drho}=frac{f(2rho)}{2f(rho)}$, I am trying to derive the form of $f(rho)$ by using a power series expansion $f(rho)=sum a_n rho^n$ and show that $f(rho)$ can be $rho$, $Rsin(rho/R)$ or $Rsinh(rho/R)$. I am getting stuck.



    What should be further steps?



    Thanks for the help in advance.






    differential-equations power-series







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      If $f(rho)$ satisfies $frac{df}{drho}=frac{f(2rho)}{2f(rho)}$, I am trying to derive the form of $f(rho)$ by using a power series expansion $f(rho)=sum a_n rho^n$ and show that $f(rho)$ can be $rho$, $Rsin(rho/R)$ or $Rsinh(rho/R)$. I am getting stuck.



      What should be further steps?



      Thanks for the help in advance.






      differential-equations power-series







      share|cite|improve this question













      If $f(rho)$ satisfies $frac{df}{drho}=frac{f(2rho)}{2f(rho)}$, I am trying to derive the form of $f(rho)$ by using a power series expansion $f(rho)=sum a_n rho^n$ and show that $f(rho)$ can be $rho$, $Rsin(rho/R)$ or $Rsinh(rho/R)$. I am getting stuck.



      What should be further steps?



      Thanks for the help in advance.






      differential-equations power-series




      differential-equations power-series






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 5 hours ago









      Tejas P

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