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Nonlinear differential equation: numerical solution


I have to find and plot a numerical solution for this second order differential equation:


u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0

where 0≤x<∞ and u(x=0)=0, limx→∞u(x)=1. How can I do it? Thank you very much.





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