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Question Number 89776 by john santu last updated on 19/Apr/20

w h a t i s t h e s t a b i l i t y o f t h e

f o l l o w i n g f u n c t i o n

\frac{d y}{d t} = y^{3} - 2 y^{2} + y

Commented by jagoll last updated on 19/Apr/20

\frac{dy}{y (y^{2} - 2 y + 1)} = dt

\frac{dy}{y {(y - 1)}^{2}} = dt

\int \frac{dy}{y {(y - 1)}^{2}} = \ln ∣ t ∣ + c

next \dots

Commented by john santu last updated on 19/Apr/20

\int (\frac{1}{y} - \frac{1}{y - 1} + \frac{1}{{(y - 1)}^{2}}) d y = \ln ∣ C t ∣

\ln ∣ \frac{y}{y - 1} ∣ - \frac{1}{y - 1} = \ln ∣ C t ∣

\frac{1}{y - 1} = \ln ∣ \frac{y}{C t (y - 1)} ∣