Question

need som help plz (DE's) ! " We live in a world where joy and empathy and pleasure are all around us, there for the noticing. Ira Glass " any way , my qs is how to know if the ODE is linear or not ? plz give an example :'(

Answer 1

This topic is usually in the very first chapter of the typical differential equations textbook. If you have a textbook, why not look up "linear differential equations:? or do an Internet search for the same topic?

Hint (not a complete "answer" and not intended to be one):

Look at the d. e. and determine the highest power to which the dependent variable, y, is raised. Similarly, determine the highest power to which the derivative of the dependent variable is raised. This information tells you whether your d. e. is linear or not. What is/are the criteria for that?

Answer 2

i dnt have a text book
and searched ( but im not good to understand)
thats why i need help :'(

Answer 3

Happy to help, but please, would you first look up "ordinary differential equations" in that textbook. In that same section you're likely to find a discussion of "first order d. e.," "second order d. e.," etc. Please type in a sentence or two from your book that describes the meaning of the word "linear" in this context. Note that I've already given you some hints:

"Look at the d. e. and determine the highest power to which the dependent variable, y, is raised. Similarly, determine the highest power to which the derivative of the dependent variable is raised. This information tells you whether your d. e. is linear or not. What is/are the criteria for that?"

Answer 4

It's a shame that you don't have a d. e. textbook. If you don't, and if you can't afford one or don't want to buy one, then you'll need to develop and use Internet search skills. The following URL will take you to a page that has some useful info.:

http://www.dummies.com/how-to/content/identifying-ordinary-partial-and-linear-differenti.html

Example !:\[\frac{ dy }{ dx }+(y)=0\] is linear because both (dy/dx) have the exponent 1.

Example 2: \[\frac{ dy }{ dx }+(y)^2=0\]

is non-linear because the dependent variable, y, is squared.

this is the kind of material you'll need to look for.

What I could do would be to help you think of appropriate search terms through which your Internet searches will provide you with the info you need.

Answer 5

well, thx alote @mathmale
@ganeshie8 explained it to me :)