Question

dy /dx + P(x) - y =Q(x) y power n
​

Answer 1

Answer:

v=

y

n−1

1

Step-by-step explanation:

An equation of the form

dx

dy

+Py=Qu

n

where P and Qare functions ofx alone or constants, is called Bernoulli's equation. Divide both the sides by y

n

, we get

y

−n

dx

dy

+Py

−n+1

=Q Put

y

−n+1

=z⇒(−n+1)y

−n

dx

dy

=

dx

dz

.

The equation reduces to

1−n

1

dx

dz

+Pz=Q⇒

dx

dz

+(1−n)Pz=Q

Which is linear in z and can be solved in the usual manner.

So the substitution is z=v=

y

n−1

1