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

$$whatisthestabilityofthe$$$$followingfunction$$$$\frac{dy}{dt}=y^3-2y^2+y$$

Commented by jagoll last updated on 19/Apr/20

$$\frac{\mathrm{dy}}{\mathrm{y}({\mathrm{y}}^2-2\mathrm{y}+1)}=\mathrm{dt}$$$$\frac{\mathrm{dy}}{\mathrm{y}{(\mathrm{y}-1)}^2}=\mathrm{dt}$$$$\int \frac{\mathrm{dy}}{\mathrm{y}{(\mathrm{y}-1)}^2}=\ln \mid \mathrm{t}\mid +\mathrm{c}$$$$\mathrm{next}...$$

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

$$\int (\frac{1}{y}-\frac{1}{y-1}+\frac{1}{{(y-1)}^2})dy=\ln \mid Ct\mid$$$$\ln \mid \frac{y}{y-1}\mid -\frac{1}{y-1}=\ln \mid Ct\mid$$$$\frac{1}{y-1}=\ln \mid \frac{y}{Ct(y-1)}\mid$$

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