= Let w1,w2 Rand let the ODE system be x = w122, x'x = -w121, ya = W242, y = -w291 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: Si = {(C1, C2) | 2} + z? = 4} et S2 = {(91, y2) | j + y = 1}. c)The torus T is parametrized using two angles (e, 0) [0, 271) * [0, 21) and x =(2 cos 0, 2 sin O) and y=(cos Lisin 9). Carry this change of variable in () to get two ODEs for (0,0). Plot some solutions in the square [0, 21) > [0, 2TT) = Let w1,w2 Rand let the ODE system be x = w122, x'x = -w121, ya = W242, y = -w291 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: Si = {(C1, C2) | 2} + z? = 4} et S2 = {(91, y2) | j + y = 1}. c)The torus T is parametrized using two angles (e, 0) [0, 271) * [0, 21) and x =(2 cos 0, 2 sin O) and y=(cos Lisin 9). Carry this change of variable in () to get two ODEs for (0,0). Plot some solutions in the square [0, 21) > [0, 2TT)