Everything With a y on One Side

You'll learnto decide whether an equation separates before you start rearranging it, to bring the constant of integration in at the one step where it belongs, and to read off what that constant becomes once you solve for y.

Separation of variables is Unit 6's integration done twice at once, and almost all of its difficulty is bookkeeping. Move every y onto the side carrying dy and every x onto the side carrying dx, integrate both sides, then solve for y. Watch one thing above all: the constant of integration enters at exactly one moment, and where it ends up decides which family of curves you have written down. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · ONE CONSTANT, AND IT ENTERS AT THE INTEGRATION · v2

the constant enters at the integration, and never after it

Before you start

What you're looking at

A derivation worked down the page, one line per click. The constant of integration is drawn in teal wherever it stands alone.

The question

Does this equation separate, and once both sides are integrated, where does that single constant end up in the answer?

Step 1 / 12