Answer
See below
Work Step by Step
Given: $y'=y(y-1)^2$
Integrate both sides:
$\int \frac{1}{y(y-1)^2}dy=\int dx$
Solve this, we get $\ln \frac{y}{y-1}-\frac{1}{y-1}=x+c$
where $c_1=0\\c_2=2\\c_3=-4$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 1 - First-Order Differential Equations - 1.12 Chapter Review - Additional Problems - Page 109: 8
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