The discussion centers on solving the Bernoulli differential equation represented by the equation 3dy/dx + y = (1 - 2x)y^4. The solution process involves substituting w = 1/y^3, leading to the transformed equation w' - w = 2x - 1. A mistake in integration was identified, which affected the final expression for y^3. The correct solution, as confirmed by Wolfram Alpha, is y^3 = -1/(-c*e^x + 2x + 1).
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bioblade said:Homework Statement
Solve: 3dy/dx+y=(1-2x)y^4
Homework Equations
None, really.
The Attempt at a Solution
y'+y/3=((1-2x)/3)y^4
y'/y^4+1/3y^3=(1-2x)/3
w=1/y^3
w'=(-3/y^4)y'
w'/-3+w/3=(1-2x)/3
w'-w=2x-1
e^int(-dx)=e^-x
e^(-x)*w=-e^-x(2x-1)+c
w=1-2x+c*e^x
y^3=1/(1-2x+c*e^x)
wolfram alpha says it should be -1/(-c*e^x+2x+1) though. What did I do wrong?