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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.3 Growth and Decay in Science and Economics, #28 · Differential Equations · Applications

A rocket has velocity

A rocket has velocity $v$ . Burnt fuel of mass $Δ m$ leaves at velocity $v - 7$ . Total momentum is constant:
$m v = (m - Δ m) (v + Δ v) + Δ m (v - 7) .$
What differential equation connects $m$ to $v$ ? Solve for $v (m)$ not $v (t)$ , starting from $v_{0} = 20$ and $m_{0} = 4$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.3 Growth and Decay in Science and Economics, #28

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