Question

My Homework is in this PDF file. Please look. How can i solve them :(

http://pdfcast.org/pdf/homework-dif-equations

Answer 1

thats a good question

Answer 2

you solve them by following the instructions given :)

Answer 3

how do we determine order?

Answer 4

then determining the order should be fairly straight forward

how is linear defined?

Answer 5

A differential equation is linear if the dependent variable and all its derivative occur linearly in the equation. But I do not know exactly

Answer 6

Please help me guys. I have exam on Wednesday.

Answer 7

so the derivatives all need to be of degree 1; nothing in powers right?

\[(y'')^2\]
is a second order; non linear; diffy q then right?

Answer 8

it is absolutely second ordar. because of second derivative of y. But i dont know is is linear or non linear? i mixed

Answer 9

the \(()^2\) around it tells us that it is not the the \(()^1\); therefore it is not linear

Answer 10

lets see if i can pull on of the problems for an example

Answer 11

1c, can you type it in here?

Answer 12

http://www.analyzemath.com/calculus/Differential_Equations/order_linearity.html look Example 2, Questions 1,2,3,4. Therefore 4. questions is hell why d3,d2 is linear and how. it is my nightmare

Answer 13

Also from my hw. 1C

Answer 14

2 and 3 of that are nonlinear; becasue; y^3 is the function itself; and is raised to a power that is NOT 1

Answer 15

3 is nonlinear since ln(y) is acting upon the function making it other than a power of 1

Answer 16

for problem 1c on the homework; its the only one thats not linear; we have:

sin(t+y) in the equation; we cant have "sin" acting on y and still be linear since it changes the "y" to a power other than 1

Answer 17

linear means; the function and all of its derivatives are raised to the power of 1; and nothing else. And as a side note, something that multiples the function with one of its derivatives makes it go nonlinear:

y y'' for example is nonlinear

Answer 18

ok how 4. question is linear (i have sent the link) . is sinx causes to it?

Answer 19

sin(x) does this contain our function and its derivatives?

Answer 20

y(x) and all of its derivates ... does sin(x) contain r alter any of the y(x) and its derivatives?

Answer 21

Please dont ask to me what and how :). i am mixed today. We just started today and these are our homework. : )

Answer 22

these are the questions you need to be asking yourself so that you can actually DO the homework :)

Answer 23

You are right. First i'll prepare coffee to myself and a cigarette. After i will ask to myself. : ) Thank for your nice answers.

Answer 24

Also my English is poor. Sorry : )

Answer 25

this is your first homework problem.
\[t^2 \frac{d^2y}{dt^2}+t\frac{dy}{dt}+2\ y = sin(t)\]

you want to ask yourself; what is my function? y(t) is our function since y is on top and t is on bottom of our derivatives

What is the highest order of derivative in the equation?

\(d^2y \) is the highest order of our derivatives so this is a 2nd order.

is it linear? I have to check to make sure NOTHING is messing with any y(t) or its derivatives. Lets look at the "variables and constants" in front of our ys and see what they do:

t^2 has no ys in it; its fine

t has no ys in it; its fine

2 has no ys in it; it fine

sin(t) has no ys in it; its fine

everything is fine so this must be linear.




ok, you have yourself a break and good luck ;)

Answer 26

The order is the highest derivative of the function!

Answer 27

superb answers : )

Answer 28

Your pdf file is too blurry to read :(

Answer 29

you do this procedure till we get to 1c and we have an issue:
\[\frac{d^2y}{dt^2}+sin(t+y)=sin(t)\]

our function is y(t) and its derivatives

d^2y is the highest order of derivative

check on the "variables and constants" in front of the y(t)s

1 ; this has no ys in it; its fine

sin(t+y) ... this DOES have a y in it; its bad

sin(t) has no y in it; its fine.

since we have an issue; with the sin(t+y) this CANNOT be linear

Answer 30

Chlorophyll you can download it from the link shown below the picture as normal pdf file : )

Answer 31

good luck :)

Answer 32

There're so many compromise when download the free file viewer, make me uncomfortable because my PC already so slow!

Answer 33

Do you have better image?

Answer 34

please click read online button from http://pdfcast.org/pdf/homework-dif-equations

Answer 35

thanks amistre64 : )

Answer 36

At first, do you understand the solution?