Question

How to check whether a dIFFERENTIAL EQUATION IS LINEAR OR NON-LINEAR?

Answer 1

Given a differential equation G(x,y,y',y",...)
G is said to be linear if x, y, y', y",... are each linear.

Answer 2

if any of the variables are squared, cubed, etc... it is not linear.

Answer 3

how do u knw each is linear?

Answer 4

wait... it looks like x can be non-linear..., but not any y variable

Answer 5

linear as in, it would make a line.... no non-unity powers in y

Answer 6

explain to me how is ths equation non-linear....yy'+2y=1+x^2

Answer 7

I think that it is the yy' term that eliminates it.

Answer 8

if one variable in unknown then a equation is said to be linear equation

Answer 9

k....thANKS....
SO WHAT U SAYING IS i HAVE TO CHECK ANY Y*Y' IN MY EQUATIONS?

Answer 10

yes... you need nice clean y variables...2y+3y'-5y".... stuff like that (official math terminology :) )

Answer 11

2y+3=5y-9 is linear equation
5q+8=78-q is linear equation

Answer 12

Thanks Euler..:)

Answer 13

I will post mre question..u seem to know a lot..lol

Answer 14

No problem... I have my diff eq book open :)

Answer 15

lol...

Answer 16

what is the name of the book? I might try to get it from my library...

Answer 17

Elemetary Differential Equations by Edwards and Penney, published by Pearson/Prentice Hall