Afunction y(t) satisfies the differential equation dy dt = y 4 − 6y 3 + 5y 2 . (a) what are the constant solutions of the equation? (recall that these have the form y = c for some constant, c.) (b) for what values of y is y increasing? (c) for what values of y is y decreasing?

Hence increasing in  (-\infty,0) U (1,5)

c) Decreasing in (0,1)

Step-by-step explanation:

Given that y(t) satisfies the differential equation

Separate the variables to have

Left side we can resolve into partial fractions

Let

Taking LCD we get

By equating coeff of y^3 we have

A+C+D=0

Hence left side =

b) y is increasing whenever dy/dt>0

dy/dt =0 at points y =0, 1 and 5

dy/dt >0 in (-\infty,0) U (1,5)

Hence increasing in  (-\infty,0) U (1,5)

c) Decreasing in (0,1)