I could use an explanation on how do identify a linear equation if you have the time. I have read the definition in the book and it is just not clicking.

Question

anonymous · Answer

A linear first order equation is an equation that can be expressed in the form
$$a _{1}(x)\frac{ dy }{ dx }+a _{0}(x)y=b(x)$$

anonymous · Answer

What class is this?

anonymous · Answer

differential Equations

anonymous · Answer

How I interpret this is everything must be in terms of x with only one term having a y.

anonymous · Answer

Kind of an elementary description

anonymous · Answer

That sounds reasonable...

anonymous · Answer

@estudier Do you have a laymens description that could be of some help.

anonymous · Answer

You are doing fine so far...(the idea of linearity extends to higher order de's as well)

anonymous · Answer

Ya I did see an example that you are describing. I thought I'd start with grasping with 1st order first

anonymous · Answer

It is as u said , y' + g(x)y = h(x)  If you can put it in this form, it's linear.

anonymous · Answer

When I look at the standard form it makes more sense. Nice I as just reading that.

anonymous · Answer

@ChmE I got pulled away, but follow @estudier for a good explanation!

anonymous · Answer

Thanks I'm going to close the question

anonymous · Answer

ur welcome