Consider the first-order separable differential equation dy/dx = y(y − 1)^2 where the domain of y...

Consider the first-order separable differential equation

dy/dx = y(y − 1)^2

where the domain of y ranges over [0, ∞).

(a) Using the partial fraction decomposition

1/(y(y − 1)^2) = 1/y −1/(y − 1) +1/((y − 1)^2)

find the general solution as an implicit function of y (do not
attempt to solve for y itself as a function of x).

(b) Draw a phase diagram for (1). Assuming the initial value y(0) =y0, find the interval of values for y0 that result in a bounded solution (that is, a function that does not get arbitrarily far away
from zero)

Expert Solution

milcah answered 2 years ago

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