On Jun 25, 12:16 am, Ondrej Certik <[email protected]> wrote:
> Well, it works for some equations already:
>
I am trying to get it to work for more cases using the general form
that I noted above (a*f(x)+log(c*f(x)+d)=b with solution f(x)=LambertW
(a*exp(b + a*d/c)/c)/a - d/c
While working through the existing patterns and others that I have
added I had the nagging feeling that there was a more general
expression that I had found, and I believe the above is it. Although I
would like to think that one of the f(x)s could be replaced with g(x),
I don't believe it's possible since in the end the equation should be
representable as F(x)exp(F(X))=k and if you have G(x)exp(F(X))=k the
only way you can change F(x) independently of G(x) is through an
additive constant (e.g. multiplying by exp(a) to change F(x) into F(x)
+a) or a multiplicative constant (e.g. multiplying by A to change G(x)
into A*G(x).
/c
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