For Questions 1–3, use the differential equation given by dx equals xy/3, y > 0.

Question

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 ? ? ? ? ? ? ? ? ?

Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4.

I need help pleasee. Thank you for the help in advance! I greatly appreciate it :)

Answer 1

#1. Really?? Given x and y, you can't compute xy/3?

I'm assuming that you meant
dy/dx = xy/3
dy/y = x/3 dx
ln y = 1/6 x^2 + ln c
y = c*e^(1/6 x^2)
Since y(0) = 4, c = 4 and so
y = 4e^(1/6 x^2)

to check, just take the derivative and verify that it equals xy/3.

Answer 2

So for number 1, is it as simple as it seems. I plug in the x and y into xy/3 and get all the values of dy/dx?