# Calculus

For Questions 1–2, use the differential equation given by dy/dx = xy/3, y > 0.
1. 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

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

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1. I think you can complete the table, right? Just plug in the values for x and y.

As for the solution, you have

dy/dx = xy/3
3y dy = x dx
3/2 y^2 = 1/2 x^2 + c
3y^2 = x^2 + c
plug in (0,4) and you have
3*16 = 0 + c
c=48

3y^2-x^2 = 48
or, in a mor standard form, you can see that you have the hyperbola

y^2/16 - x^2/48 = 1

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