Ivan Shishkin, Rye (1878)

Problems/Linear algebra

Équation différentielle à solutions polynomiales

by SalixBabylonica·
42
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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ReviewedReviewed by Ancient Tree
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This problem was submitted to “Differential equations”.

Showing the Français version because no English translation exists yet. Add that translation.

Soient a,b∈Ka,b\in\mathbb{K} et n∈Nn\in\mathbb{N}.
Déterminer tous les polynômes P∈K[X]P\in\mathbb{K}[X] de degré nn vérifiant
nP(X)=(X−a)P′(X)+bP′′(X).nP(X)=(X-a)P'(X)+bP''(X).

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