Answer:
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)