I am trying to solve the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

##\frac{d^{2}y}{dr^2}+(\frac{1}{r}+1)y=0##

with the boundary conditions

##y(r) \rightarrow r \frac{dy}{dr}(0)## as ##r \rightarrow 0## and ##y(r) \rightarrow \sin(kr+\delta)## as ##r \rightarrow \infty##.

I know that the shooting method is the way to go, but am having trouble figuring out how to implement the boundary conditions.

Are the following lines of code in Mathematica alright? I have not yet wrapped it around a root-finding algorithm.

diffeq = {y''[r] + ((1/r) + 1) y[r] == 0, y[0] == 0, y'[0] == 5};

sol = NDSolve[diffeq, y, {r, 0, 200}, Method -> "ExplicitRungeKutta"];

Now, how do I change y[0]=0 in the code above to the first boundary condition.

Also, I know that the value of y[0] is to be changed and the code run until the second boundary condition is satisfied. What check should I use for that? Do I just check if the solution lies between -1 and 1 as ##r \rightarrow \infty##

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# Boundary conditions shooting method

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