(a) One of the many types of differential equations we have not considered in class is the unfortunately named (since there are several other equations with the same name) Bernoulli (differential) equation, which is a differential equation which can be written in the form
dy
dx + P(x)y = Q(x)y
n
where n is a real number. Research Bernoulli differential equations and use the knowledge
you gain to solve the following Bernoulli differential equation for y(t):
(1 − t
2
)
dy
dt − ty = 5ty2
.
You may assume 1 − t
2 > 0