Question: Solving ODE numerically

Hi. I am trying to identify mode shapes (phi(x)) and natural frequencies  of non-uniform euler-bernoulli beam. There are number of numerical methods to solve ODE with certain boundary conditions (i.e. Runge Kutta method). Problem is that I am newbie here. I am interested in particularly first vibration mode and its frequency. Is there anyone acquainted with it and would be able to help me?  Non-unif.mw

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