An email posed the following problem: Given the equation and the function F(x,y)=0 , solve the equation for y=y(x) and evaluate G(x,y(x)). A further email asked for the computation of G’(x,y(x)).
Well, if the function F is amenable, then this is something that requires no more than basic algebra and calculus. But the example function F given was not amenable, and only a numeric solution would suffice. Could it be done easily in Maple?
This video will show how it could be done, and done with the simplest of Maple syntax and constructions. Nothing fancy, and no Maple coding.
Now while working out a solution in respose to the email, a recollection cane to mind of the Draghilev (Dragilev?) method for parametrizing the solution of n equations in n + 1 unknowns. Each of the n + 1 unknowns is parametrized (say, by t) and found as the solution of a set of n + 1 initial value problems. But the given problem has just 1 equation and n+1=2 unknowns. Could the Draghilev method by applied, and would it or would it not be an improvement?
Well, this video will look at the Draghilev method and answer the question of utility. I'm sure you want to know the answer as much as I did.
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