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I am looking at the Ritz method for the following problem

##\displaystyle -\frac{d^2 u}{dx^2}-u+x^2=0## for ##0<x<1##

with boundary conditions ##u(0)=0## and ##\displaystyle \frac{du}{dx} |_{x=1} =1##

The last derivative term, how do I know whether that is a natural or essential BC?

I have googled the following guidelines but I am still confused.

Specification of the primary variable ( u in this case) is an essential BC*

Specification of a secondary variable (like a force F, not present in this example) is a natural boundary condition

IF a boundary condition involves one or more variables in a 'direct' way it is essential otherwise it is natural.

Direct implies excluding derivative of the primary function.**

I find this info conflicting based on * and **

I think the book states it is a natural BC.

Would appreciate some clarification...

THanks

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# Difference between Essential a Natural BC's

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