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Sunday, 22 October 2023

Most general `wave' equation

Prototype: u(x,t)=f(xvt) 

g(x,t)=f(x(t0))=f(x(t)±n=1f(n)(0)n!xn)

(Taylor series)

or, Prototype: u(x,t)=f(vat) 

dn+1xdtn+1(t)=0

then

p(dnxdtn,t)=h(dnxdtn(t)±tddtdn1xdtn1(t)).

(Taylor approximation)

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