edifferentielle.py

Created by klfraimbow

Created on April 03, 2022

646 Bytes

PREMIER ORDRE
a y'(t)+ b y= d(t) 
E1:

Yo(t) = ke**-A
A= b/a

E2:
  g'(t)=... do,c g'(t)-g(t)=...

E3: 
  y(t)=Yo + Yp
y(t)=yo(t)+g(t)
E4:
  
2ND ORDRE
a y''(t) + b y'(t) + c y(t)= P(t)e**mt

E1 : e homogene
  a y''(t) + b y'(t) + c y(t)=0
at**2+bt+c=0     disriminimant delta: b**2-4ac

Delta >0 r1= -b-sqrtdelta /2a   r2= -b+sqrtdelta /2a
Yo(t)= C1* e**r1t +C2* e**r2t
C1 C2 reels

Delta =0 r0= -b/2a
Yo(t)=(C1t+C2)* e**rOt

Delta <0 z1= -b-isqrtIdeltaI /2a
= alpha-iBeta et Z2= alpaha+iBeta
Yo(t)=(C1cos(beta*t)+C2sin(beta*t))* e**alpha*t




exo
f(t)=C1e**-3t + C2e**t + te**2t
f'(t)=-3C1e**-3t + C2e**t + e**2t *(1+2t)

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