Question

how to determine if the diff Eq is linear or non-linear

Answer 1

if its contain y' and like normal polynomial variabels then its linear like :-

y'+1=C
Y'+y=x
y'=e^x

non linear like
y''+y'+1=0
y''=ye^x
y'' e^x+y ln y =c

Answer 2

nice @ikram002p :)

Answer 3

XD

Answer 4

example: \[xy^{(5)}+x^2y^{(3)}+\sin(x)y^'-y=e^x\] where y is a function of x

Answer 5

Linear can be any degree, but you will never multiply the y terms. In fact, all of the y terms will be on their own, multiplied by either a constant or a function of x:

\[P(x) y'' + Q(x) y' +R(x) y = f(x)\]

Answer 6

\[xy^{(5)}+x^2y^{(3)}+\sin(x) y^{'}-y=e^x\]

Answer 7

You will never have something like y^2, sin(y''), or y/y''.

Answer 8

so the above example is non-linear right?

Answer 9

because y' is multiplied by the sin(x)

Answer 10

No, that is linear (because it's multiplied by a function of x, it's OK)

Answer 11

why this is non-linear dx/dt=x^2

Answer 12

is it becauyse there is no function related to time?

Answer 13

Since the variable we're taking derivatives of is the same variable that's squared.

Answer 14

got you