demonst.py

Created on November 14, 2024

582 Bytes

Sens direct : Si f est solution de 
(E). On montre que f-P est 
solution de (E')
on calcule : 
(f-P)'=f'-P'=af+-aP-=a(f-P) 
donc (f-P) est bien solution de 
(E').
Sens réciproque : Si f-P est 
solution de (E'), on montre que 
f est solution de (E)
on sait que (f-P)'=a(f-P) donc 
f'-P'=af-aP et f'=af+P'-aP
or P'-aP= donc f'=af+, ce qui 
veut dire que f est solution de 
(E).

Ainsi si f est solution de (E) 
alors f-P est solution de (E'), 
or les solutions de (E') sont 
Keax
alors f-P=Keax et on en déduit 
que f(x)=Keax+P où P est une 
solution particulière.

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demonst.py