Question

plz help :(
i will love +fan +medal
or what ever u want
determine if these equation linear or not (explain why )

Answer 1

\(\Huge y'''+2e^ty''+yy'=t^4\)

Answer 2

a linear equation is linear in "y" and "its derivatives"

Answer 3

so, for an equation to be linear there should not be any second degree terms like :
yy' or yy'' or y^2

Answer 4

mmm why yy' not linear ?

Answer 5

let me ask u a question, how does a linear equation in "x, y, z" look like ?

Answer 6

ax + by + cz = d

Answer 7

where a, b, c are constants right ?

Answer 8

why there are not xy or yz terms in it ?

Answer 9

ok right ?!

Answer 10

right !

Answer 11

awesome explanation

Answer 12

lol @mlb004 are u a cheerleader :P

Answer 13

A linear DE is an equation in "y" and "its derivatives", so you should not see any product terms in the equation

yy' is a product of two variables y and y'
yy" is a product of two variables y and y''
y^2 is obviously not linear

Answer 14

think of y, y', y'', y''' etc... as variables

Answer 15

that makes it easy to spot the linearity

Answer 16

yes !
i got it XD
thx alote !
as mlb004 said awesome <3

Answer 17

np :)