Question

(1 point) Suppose (a) Find cy and c2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? Choose (c) What is the approximate direction of travel for the solution curve, as t increases from -oo to -+o0? A. along the line y the origin z toward the origin and then along the line y z away from B. along the line y toward the origin and then along the line y r away from the origin C. none of the above Note: In order to ger credit for this probiem all answers must be corect ㄇ

Answer 1

Given y vector (t0 = c_1 e^- t (1 - 1) + c_2 e^t (1 1) and y vector (1) = (- 2 0) (a) now applying initial conditions we have y vector (t) = c_1 e^- t (1 - 1) + c_2 e^t (1 1) implies y vector (1) = c_1 e^- t (1 - 1) + c_2 e^t (1 1) implies (- 2 0) = 0.36788 c_1 (1 - 1) + 2.7183 c_2 (1 1) implies (- 2 0) = (0.36788 c_1 - 0.36788 c_1) + (2.7183c_2 2.7183c_2) implies (- 2 0) = (0.36788 c_1 + 2.7183 c_2 - 0.36788c_1 2.7183 c_2) by solving we get c_1 = -5.4365 c_2 = 0.