Identifying First Order Diff Equations

So the equation is

It says to identify is the equation is Bernoulli, Separable, Linear and Homogeneous

If these definitions are wrong on how to identify which is which, please let me know, because i researched this because my professor doesn't teach well.

Bernoulli -

Separable - where p and h are functions (I don't really understand this one too much.)

Homogeneous - Look at the degrees of each grouping of coefficients, if they are all the same means homogeneous (Ex. , so all the coefficient grouping ignoring y' are 3)

Linear - where P and Q are continuous functions

So

Wouldn't I manipulate this to and that would be linear

Also

How did you come up with the conclusion you did for each one?

Re: Identifying First Order Diff Equations

Quote:

Originally Posted by

**bustacap09** So the equation is

It says to identify is the equation is Bernoulli, Separable, Linear and Homogeneous

If these definitions are wrong on how to identify which is which, please let me know, because i researched this because my professor doesn't teach well.

Bernoulli -

Separable -

where p and h are functions (I don't really understand this one too much.)

Homogeneous - Look at the degrees of each grouping of coefficients, if they are all the same means homogeneous (Ex.

, so all the coefficient grouping ignoring y' are 3)

Linear -

where P and Q are continuous functions

So

Wouldn't I manipulate this to

and that would be linear

Also

How did you come up with the conclusion you did for each one?

If you factor the original equation you get

What does this tell you?