Question

Determine the general solution by solving the ODE system

2r+y

Answer 1

Given that dx/dt = 2x + y dy/dt = -n + 4y that is(1) compare with dx/dt = a_1x + b_1y dy/dt = a_2x + b_2y and its auxiliary equation is given by m^2_(a - 1 + b_2)m + (a_1b_2 - a_2b_2) = 0 here a_1 = 2, b_1 = 1 a_2 = -1, b_2 = 4 so m^2 - (2 + 4)m + (2.4 - (-1) 1) = 0 implies m^2 - 6m + 9 = 0 m^2 - 3m - 3m + 9 = 0 m(m - 3) - 3(m - 3) = 0 m = 3,3 repeated roots In this we have the one solution x = A e^mt, y = B e^mt the Associated linear algebraic system of (1) is (2 - m)A + 1B = 0 - A + 94 - m)B = 0 now For m = 3 - A + B = 0 & -A + B = 0 A = B