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nombres complexes


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QCM 5

attention c'est cos(α) = sin(α + π/2), cos(α + π/2) = -sin(α)

⇒ D est faux

 

QCM 6

f'(t) + f(t) = 2

 

1) On commence par résoudre l'équation homogène fh'(t) + fh(t) = 0:

fh(t) = k e^-t

 

2) On cherche une solution particulière fp(t) de l'équation totale f'(t) + f(t) = 2:

fp(t) = 2 convient

 

3) Les solutions de f'(t) + f(t) = 2 sont fp(t) + fh(t):

f(t) = 2 + k e^-t

avec k réel qui dépend des conditions initiales

 

4) Si f(0) = 3:

f(0) = 2 + k e^0 ⇒ 3 = 2 + k ⇒ k= 1 ⇒ f(t) = 2 + e^-t

⇒ B vrai, D faux, E faux

 

si ton cours n'est pas bien clair: https://www.methodemaths.fr/equadiff/

 

 

 

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