Thread: Graphing differential equations in general

I am having trouble recalling how to graph things. In class, we are learning about autonomous equations and population dynamics, and a big part of this portion of the class is about graphing the equation, finding critical values, and drawing phase lines. My problem is, I've been away from math for so long, I've forgotten how to graph things by looking at the equations!

In particular, I am having problems graphing:

dy/dt = ay +by^2, a>0, b>0, -infinite< y-knot < infinite

and

dy/dt = y(y-1)(y-2), y-knot >= 0

Please, please, please link me to any resources that have a decent tutorial about how to graph things. Much appreciated!!!

Have you tried to solve these equations?

You should be able to apply the separation of variables, decompose using partial fractions then integrate.

This looked relevant. Do you not have any equations for x's? For example: dx/dt = ...?

This also looked relevant. That first link was for MATLAB. For Mathematica, try this. For Maple, go here or here.