Question

use the differential equation given by dx equals x times y divided by 3, y > 0.
Complete the table of values
x −1 −1 −1 0 0 0 1 1 1
y 1 2 3 1 2 3 1 2 3
dy, dx
and also
Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4.
I don't need the solutions, I just need to know how to do them, any help is appreciated!

Answer 1

well, your table should be dx = xy/3 but its hard to see how to place them

is x a function of y or some other random variable?

Answer 2

oh, it says y=f(x)

Answer 3

ive got nothing without a clear picture of the problem ..

Answer 4

So it's not just me, thats the exact question typed up, I feel like my teacher pulled this question from the internet and didn't really think about it, I don't know how to do this question. Here is a picture of the question with proper formatting.

Answer 5

@amistre64 Any clue,I still don't understand how to do this question, It's the only one I have left.

Answer 6

thats better ..... the pic that is

dy/dx is defined by xy/3 they give you xy, multiply them together and divide by 3 to determine dy/dx

Answer 7

dy/dx = xy/3

dy/dx = -1(1)/3
dy/dx = -1(2)/3
dy/dx = -1(3)/3
dy/dx = 0(1)/3
dy/dx = 0(2)/3
dy/dx = 0(3)/3
dy/dx = 1(1)/3
dy/dx = 1(2)/3
dy/dx = 1(3)/3

Answer 8

y' = xy/3 is a sovlable diffy q on its own ... dunno what the table would be for

Answer 9

dy/dx = xy/3, its seperable, so seperate it

3 dy/y = x dx

integrate it

3 lny = 1/2 x^2 + K

and solve for y

y = Ce^(x^2 /6)

now define C using the intial condition ....

its a very basic process here

Answer 10

Thank you, I was confused and you cleared it up