Let w1, w2 R and let the ODE system be x = 81x2, x2 = -w1x1, y = W2y2, 32 = -W241. Do not solve the EDO. a) Find three non-trivial prime integrals that are two by two linearly independent. b) We consider a circle in the plane x1x2 and in yly2: S = {(x1, x2) | x + x = 4} et S2 = {(1, 2) | y + y = 1}. c) The torus T is parametrized using two angles (0, ) [0, 2) [0, 2) and x =(2 cos 0, 2 sin 0) and y=(cos sin ). Carry this change of variable in () to get two ODEs for (0, p). Plot some solutions in the square [0, 2) [0, 2)