Solve −B\ln y−Ay\ln y+Ay−A=0 for y

David Lewis

David Lewis

Answered question

2022-01-22

Solve BlnyAylny+AyA=0 for y

Answer & Explanation

Nadine Salcido

Nadine Salcido

Beginner2022-01-22Added 34 answers

Hint:
0=BlogyAylogy+AyA=log1yB+log1yAy+Ay+A=log1yAy+B+Ay+A
This doesnt
Tiefdruckot

Tiefdruckot

Beginner2022-01-23Added 46 answers

Changing variable log(y)=x the equation can be taken in the form:
ex=BAx+ABx1
Such equation can be formally solved by Lagrange series (related to Lambert W function):
x(a,b)=t(ts)n=1Ln(n(ts))nentan
where:
Ln(x) is n-th Laguerre polynomial and Ln(x) its first derivative
where:
s=AB
t=1
a=BA

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