(Page 313, 6.3 Computer Problems, 1(a,d)) Apply Euler's Method with step sizes At = 0.1 and St = 0.01 to the following two initial value problems: Y₁ = y₁ + y2 1 = 31+32 Y2 = −Y₁ + y2 y2 = 2y1 + 2y2 y₁ (0) 1 y₁ (0) = 5 Y2 (0) - 0 Y₂ (0) = 0 One can verify that the exact solutions are Y1 et cost = Y₁ = 3e-t +2e4t Y/₂ == - et sint Y2 = -2e-t +2e4t respectively. Plot the approximate solutions and the correct solution on [0, 1], and find the global truncation error at t = 1. Is the reduction in error for At = 0.01 consistent with the order of Euler's Method? [3 marks]