Lyra recognized the form. It was a first-order linear ODE. She rewrote it:
The left side was a perfect derivative:
The Churnheart wasn’t a normal vortex. Its radial velocity ( v(r) ) at a distance ( r ) from the center obeyed a differential equation that had baffled engineers for decades:
[ \frac{dv}{dr} + \frac{1}{r} v = 3r^2 ]
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 ]
