What has always irked me when doing maths is that I seem have not been able to get a proper grasp of the actual visual changes of a calculus process, without explicit solving.  Take this equation for example.

This differential equation when solved produces this rather nice function:

Given it is an initial value problem, solutions such as the following can be derived:

Which can then allow you to determine facts about the function, such as the expected behaviour as t tends to zero with (0,2).  This is fun at all, but how do I actually do this implicitly, when such insight is absent?

16 hours ago  /  0 notes