Question

State the order of the given ordinary differential equation. (1 − x)y'' − 7xy' + 9y = cos x
And then it says

Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1.

Answer 1

order of DE is the Largest derivative present in DE.
its y''
so 2nd order.
since there is no power of derivative and no product of dependent variable with derivative ,the power of dependent variable (y) is also 1 .
so it is linear Equation.

Answer 2

When I put second order in for my answer on webassign it was wrong so I didn't know if I was right. Is it just whatever the highest derivative in the problem is the order?
Can you explain a little about whether or not its linear?

Answer 3

see condition for linear is that it should be of degree 1 and should not have product of dependent variable with derivative

Answer 4

This one is linear tho, is there a way to test it, or do I just need to memorize the conditions?

Answer 5

@ashleyfallon7 u should even memorize the test .....lol..........
@saadi u r right!!!!!!!

Answer 6

the equation is non linear if
1) the power of dependent variable is more than 1.
2) there is power of derivative
3) id there is dependent variable Multiplied with derivative
following are examples
1) (y'')^2+3y'+4=0 (because there is power of derivative)
2) y''+5y^2=0 bcz the power of dependent variable is more than one
3) y*y''+7y'+6y=0 bcz there is product of derivative with dependent variable.
i hope this help you.

Answer 7

I get it now, I didn't realize what you meant at first about the power of the derivative!! Thanks tho!! So if any or all of the derivatives are raised to a power then it makes it nonlinear and if they are not raised it is linear......right? Thank you so much ladies!

Answer 8

all of the above three examples are non linear Odes of second order.

Answer 9

@ashleyfallon7 even the derivative should not be multiplied vth the dependent variable.......

Answer 10

Thank you all! I'm taking DE for the first time and the terminology is harder to get than the math! I understand now, thank you @anusha.p, @saadi, @manishsatywali

Answer 11

u r welcome:)

Answer 12

here i toatlly disagree with @saadi '''power of derivative'''''''' doesn't affect linearity

Answer 13

@manishsatywali saadi is right.....
u check urself once...

Answer 14

a(d^2x/dt^2)+b(dx/dt)+cx=d

Here x is the variable and the derivatives are with respect to a second variable t. The letters a, b, c and d are taken to be constants here. This equation would be described as a second order, linear differential equation with constant coefficients. It is second order because of the highest order derivative present, linear because none of the derivatives are raised to a power, and the multipliers of the derivatives are constant.

I found this after @saadi explained her answer to me so I would agree that she is correct.