Lyra recognized the form. It was a first-order linear ODE. She rewrote it:
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: Integral calculus including differential equations
[ \frac{dv}{dr} + \frac{v}{r} = 3r^2 ]
[ v(r) = \frac{3}{4} r^3 ]