Question

I need help identifying what type of differential equation theses examples are (simple,separable,linear, or homogeneous)

dy/dx=3y+x^2
dy/dx=3yx^2
dy/dx=3x+x^2
dy/dx=3y+1
dy/dx=(3y+x)/(y-x)
dy/dx=(3y+x^2)/(y-x)
dy/dx=(3y+1)/(1-x)

Answer 1

Rather than give you the answers, much better to ask you: what are the definitions and examples of each of those terms.

Then I'd be happy to analyze a couple of these equations with you to see whether or not they meet those defintions

Answer 2

okay great this is what i have so far
dy/dx=3yx^2 is a separable differential equation
dy/dx=3y+x^2 is linear d.e.
dy/dx=3x+x^2 is a simple d.e.
dy/dx=(3y+1)/(1-x) is a separable and homogenous d.e

Answer 3

All of those are correct.

Answer 4

alright awesome so the ones i am unsure on are
dy/dx=3y+1 maybe a simple d.e?
dy/dx=(3y+x)/(y-x)
dy/dx=(3y+x^2)/(y-x)

our teacher told us some of theses may be ones we haven't discussed

Answer 5

Of these three: the first is linear, separable and inhomogeneous; the second and third are not simple, non-linear, inhomogeneous, and not separable.

Answer 6

The last one is separable.

Answer 7

That is , the last one in your original post.

Answer 8

how do you know if a d.e. is linear i think im alil confused on that

Answer 9

An equation is linear if all the powers of y, y', y'', y''', ... are only one.

So y' + y = x is linear
But y' + y^2 = 0 is not, nor y' + 1/y = x

You have to be careful though and write things out (on paper or in your mind), because this equation is linear, for instance: y'/y + x = x^2

Answer 10

oh okay that helps clear some things up for me, thanks!

Answer 11

Technically, get all the terms of y one side of the equals sign and set them equal to zero. If you can substitute y = ky where k is a scalar into the equation and keep equality, then the equation is linear.

For instance in my first equation above

(ky)' + ky = 0 => k(y' + y) = 0 => y' + y = 0

so the equation is linear.

But for y' + y^2 = 0, (ky)' + (ky)^2 = ky' + k^2.y^2 = 0 from which we can't deduce the original form

Answer 12

Awesome! that helps alot i didn't take good notes on linear d.e. thanks again for your help