Differential Equations question

[Newbatmath]

Homework Statement

Use a CAS and knowledge of level curves to plot representative graphs of the members of the family of solutions of the differential equation. Experiment with different numbers of level curves as well as various rectanguar regions defined by a<x<b,c<y<d. Then on separate coordinate axes plot the graphs of the particular solutions corresponding to the initial conditions: y(0)=-1, y(0)=2 y(-1)=4, y(-1)=-3

Homework Equations

Differential equation: dy/dx = -(8x+5)/(3y^2+1)

The Attempt at a Solution

This totally confuses me as the textbook never once mentions level curves or even family of solutions. What do these terms mean? I'm starting to think online college isn't the right course method for me. The second part (then on separate coordinate axes plot the graphs of the particular...) do we just solve the diff with x=0,0,-1,-1 and y=-1,2,4,-3?

 

[CFDFEAGURU]

Here is a link to some pretty good online notes. They might help you out.

http://tutorial.math.lamar.edu/Classes/DE/DirectionFields.aspx

Thanks
Matt