What is the difference between first order linear equations and seperable equations?

Question

I want to be able to recongnize a linear equation from and seperable equation. For a test.

Answer 1

A first order linear differential equation can be written in the form

dy/dt+p(t)y=q(t).

If q(t) is identically the zero function, the equation is said to be homogeneous.

A first order differential equation is separable if it can be written in the form

dy/dt=f(y)g(t) or, equivalently, as f(y)dy=g(t) dt.

Observe that a first order linear equation is separable if and only if it is homogeneous.

You can spot separable equations: there are only products involving the two variables; never sums or differences.

So, dy/dt=y t is separable and linear
dy/dt=y+t is linear but not sepable
dy/dt=y^2t^2 is separable but not linear
dy/dt=y^2+t^2 is neither linear or separable

Good luck on your test!

Answer 2

In ODE's a linear equation will be an equation where your biggest power is dy/dx. There will be no terms in dy^2/d^2x or above. There are easy to recognize by that simple fact. As for seperable, well the name says it, there is a way to split the equation so that all the y's are on 1 side and all the x's on the other. Even the dy's and the dx's. You really want these 2 types to show up on the test, they are easiest to see.

Answer 3

First order means that you have a differential equation in which the highest power of a differential is 1. e.g. you have dy/dx but not d^2y/dx^2, d^3y/dx^3, etc.

Separation is a solving-recipe that works on certain differential equations regardless of the order.

Answer 4

Linear equation

is an equation whos variables or variables is of the first degree. A stright line is the graph

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Seperable Equations

www.sosmath.com/diffeq/first/separable/separable.html

Answer 5

Pudding

Answer 6

They don't relate.