One Curve Out of Infinitely Many

You'll learnto turn a general solution into a particular one with the point you were given, to let the sign of that point choose the branch, and to say on what interval the answer is actually a function.

The general solution is a family of curves. An initial condition picks out one member of it, and doing that properly means three things rather than one: solving for the constant, deciding which branch of the answer the point sits on, and saying on what interval the result is defined at all. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · SOLVE FOR C, PICK THE BRANCH, NAME THE INTERVAL · v2

one point names one curve, one branch and one interval

Before you start

What you're looking at

A family of curves, all of which solve the same differential equation, and one marked point.

The question

Which member does the given point name, which branch of it does the sign of that point choose, and how far does that member actually reach?

Step 1 / 12