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Question: How does Maple arrive at an implicit solution to int[y'(x)*w(x)] = [ int( [y(x)^(1/2]*w(x)]^(-2/3)?

Question:How does Maple arrive at an implicit solution to int[y'(x)*w(x)] = [ int( [y(x)^(1/2]*w(x)]^(-2/3)?

Joseph Poveromo 25 Maple
October 04 2023
0
Equation:=int(y'(x)*w(x)) = [int([y(x)^(1/2)]*w(x))]^(-2/3) When plugging this Equation into dsolve, Maple provides the following implicit solution: Solution:= [3*y(x)^(4/3)]/4 + int[(2*y(x)^(5/6)/[3*int([(y(x)^(1/2))*w(x)]/[3*int[(y(x)^(1/2))*w(x)]^(5/3) When going to odeadvisor, the suggestion was to first convert to the form y = G(x,y'(x) and then utilize the method of 'patterns', which I could not apply to this equation. If anyone can fill in the steps between 'Equation' and 'Solution', it would be greatly, appreciated. P.S.Sadly, I am unable to attach the actual Maplesoft worksheet.
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