Question: Problem 7. (11 POINTS) CONSIDER A NONLINEAR SYSTEM OF DIFFERENTIAL EQUATIONS WITH POSITIVE NUMBERS C > 0 AND w > 0: x = y, y'

Problem 7. (11 POINTS) CONSIDER A NONLINEAR SYSTEM OF DIFFERENTIAL EQUATIONS

Problem 7. (11 POINTS) CONSIDER A NONLINEAR SYSTEM OF DIFFERENTIAL EQUATIONS WITH POSITIVE NUMBERS C > 0 AND w > 0: x = y, y' = -cy - w sin(x) WHICH STATEMENT IS NOT CORRECT? (A) THE SYSTEM HAS INFINITELY MANY CRITICAL POINTS. (B) THE POINT (37, 0) IS AN UNSTABLE SADDLE POINT FOR ANY VALUES OF C AND W. (C) IF c = 5 AND W = 2, AND INITIAL CONDITIONS ARE (0) = 199T/100 AND y(0) = 0, THEN lim y (t) = 0. (D) IF INITIAL CONDITIONS ARE r(0) = 7 AND y(0) = 27, THEN lim (t) = 7 FOR SOME t-too C AND W

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