methao.py

Created by arthurboubault

Created on February 08, 2022

641 Bytes

La solution gÈnÈrale de líÈquation di§Èrentielle 
 ay0 + by = 0 est
y = Cert  avec cste et r = b/a sol
d l'EC: ar+b=0

La solution de líÈquation y'' + w^2y = 0 
est y = A sin(wt) + B cos(wt)
o ̆ A et B sont deux constantes 
(Èquation de líoscillateur harmonique).
    
sol de ay'' +by' +cy = 0
líÈquation caractÈristique ar2 + br + c = 0
en remplaÁant y par 1, y' par r et
y'' par r^2
si delta>0:
  deux racines -b+-racine delta/2a
  sol= y = Aer1t + Ber2t
delta=0 :
  1 rac = -b/2a
  sol = y = ert (At + B)
delta <0:
  r=alpha+ibeta et r/= alpha-ibeta
  sol y=  ealphat [A sin (betat) + B cos (betat)]

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