Solving indexed ODE in Mathematica

Question

I would like to solve an ODE with indexed variables symbolically. Is there a way to do that?
$$frac{dp_{betaalpha}}{dt}=mleft(p_{1alpha}p_{beta2}+p_{2alpha}p_{beta1}right)$$
m is called mass and is constant. t is time.

Henrik Schumacher · Answer

I don't think that there is a direct way, by you can generate the list of equations programmatically, e.g., with
Flatten@Table[
  p[β, α]'[t] == m (p[1, α][t] p[β, 2][t] + p[2, α][t] p[β, 1][t]),
  {α, 1, 2}, {β, 1, 2}
  ]

Afterwards, you can apply DSolve or NDSolve to solve them (
suitable initial conditions provided).

Solving indexed ODE in Mathematica

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