I'm trying to solve the following boundary value problem with shooting method. Can someone help me?

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hao chen
hao chen on 31 Dec 2020
I want to find the value 'k' for a specific value of 'R', i.e., the function k(R).
For example, when R=1, I solved the 'k' about 1.34. But when , it seems uneasy.
So can someone help me solve this fourth-order ODE with the boundary value problem?

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