[ r \frac{dv}{dr} + v = 3r^3 ]
Now came the integral calculus. The total destructive potential ( P ) was the integral of velocity across the whirlpool’s radius ( R ) (which was 4 meters): Integral calculus including differential equations
[ \frac{dv}{dr} + \frac{v}{r} = 3r^2 ]
The integrating factor ( \mu(r) ) was:
The left side was a perfect derivative:
Lyra paused. At the center ( r \to 0 ), velocity couldn’t be infinite (no whirlpool tears a hole in reality). So ( C = 0 ). The true function was clean and smooth: [ r \frac{dv}{dr} + v = 3r^3 ]
"48 flux-units," she whispered.