I am trying to solve below equation, but DSolve gives two different solutions an I don't know which one should I choose. Could anyone help me? My code is as below

DSolve[f'[r]/r + f''[r] == -A Exp[-B f[r]], f[r], r]

Boundary conditions are also known:

f'[R]= d
Integrate[r Exp[-B f[r]]= e,{r,0,R}]
  • $\begingroup$ What are the boundary conditions? $\endgroup$ May 15, 2018 at 18:22
  • $\begingroup$ I know f'[r] in r=R and one other condition which is complicated @AccidentalFourierTransform $\endgroup$ May 15, 2018 at 18:24
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    $\begingroup$ @HolgerMate x^2-1=0 It should only have one solution? $\endgroup$ May 15, 2018 at 18:41
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    $\begingroup$ There is uniqueness theory for 1st order ODE's. All second order ODE's can be converted to 1st order ODE. One of your 1st order ODE's is non-linear. You need to lookup uniqueness theory for non-linear first order ODE's. It also depends on the interval of the solution. $\endgroup$
    – Nasser
    May 15, 2018 at 18:56
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    $\begingroup$ In any case, if you want $f(r)$ to be well-behaved around $r=0$, you need to take C[1] -> 0. $\endgroup$ May 15, 2018 at 19:02


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