3. Consider the differential equation * = -2y+(1 (1) v=2s+v( 15 1-25 9 (a) Rewrite (1) in polar coordinates (b) Find (0,

[answerhappygod]

3 Consider The Differential Equation 2y 1 1 V 2s V 15 1 25 9 A Rewrite 1 In Polar Coordinates B Find 0 1 (29.04 KiB) Viewed 26 times

3. Consider the differential equation * = -2y+(1 (1) v=2s+v( 15 1-25 9 (a) Rewrite (1) in polar coordinates (b) Find (0,00) +R?, t+ (r(t), 8(t)), the general solution of the differential equation r=r- (2) = 2 given in polar coordinates such that F41) . (c) Using the result from (b), show that (2) bas a non-trivial closed orbit. [3 marks) 1/2 (d) In polar coordinates, let (troy : (0,0) + R2, (r(t,ro), e(t) with r(t, rol 3[1+(8 - 1)e ]" and 8(t) = 24 with ro = r(0)>0. Find to such that y(t,ro) is a parametrisation of a closed curver, and then use its Poincare map to show that I is stable. (10 marks)