differenciel.py

Created by mathoulde1406

Created on December 18, 2023

688 Bytes

- resolution eq diff y'=ay+b
1 sol G : C(e^ax)-b/a=y(x)
2 sol part
  on cherche C (y(0)=5) on resout
  on ecrit la sol avec C 

- resol eq diff 2ordre y"+w2y=0
1 sol G f(x)=y=Acos(ws)+bsin(wx)
  - par identification w2=? w=rac?
  - on ecrit la sg en remplacent w pour 
  y et y'
2 sol P 
on cherche A et B, deux etapes 
 y(0) on resout on trouve A
 y'(0)on derive et on resout on troyve B

cos(u)'=u'sin(u)
sin(u)'=u'cos(u)
sin(0)=0 et cos(0)=1

resol d'un trinome y"+ay'+by=0
si Dsup0 y=f(x)=Ae^r1x + Be^r2x
si D=0 (Ax +B)e^rx
si Dinf0 R1=d+jB et R2=d-jB
        y=e^ax fois (Acos(Bx)+ Bsin(Bx))

- pour verifier qu'une fonction estb solution 
on regard si ca fait 0

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