Complete the Table of Values using Differntial Equation: find dy/dx = xy/3, given x,y

[IceJckson]

I'm gonna be honest, I don't really understand what I'm supposed to find for this problem?

"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."

 

[tkhunny]

I'm gonna be honest, I don't really understand what I'm supposed to find for this problem?

"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."

Have you considered calculating xy/3 for each combination of x and y?

 

[HallsofIvy]

Part (a) is almost trivial. You are told that dy/dx= xy/3, are given a list of x and y values, and are asked to find the corresponding value of dy/dx. As tkhunny suggested, just calculate xy/3 for each x, y pair.

Part (b) asks you to solve the equation with y(0)= 4. From dy/dx= xy/3, 3dy/y= xdx. What do you get when you integrate both sides? Don't forget the "constant of integration". Use y(0)= 4 to determine that constant.