Outside the high school program / Differential equations 1 exercises corrected

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1. Unclassified financial years E.3651 Consider the following two differ-ential equations defined on − ı 2 ; ı 2 : ( E ) : y + 1 + tan x y = cos x ( E 0 ) : y + y = 1 1 Give the set of solutions to the equation ( E 0 ) . 2 Let f and g be two functions derivable on − ı 2 ; ı 2 and such that : f ( x ) = g ( x ) cos x Show that the function f is a solution of ( E ) if and only if the function g is a solution of ( E 0 ) . 3 Determine the f solution of ( E ) such that f (0)=0 . https://chingmath.fr sacados/3651 Metropole et Reunion Septembre 2007 4 points