1. The differential equation +34 + 2x = 0 has the general solution x(1) = c1e+c2e-2# (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we...

Extracted text: 1. The differential equation +34 + 2x = 0 has the general solution x(1) = c1e+c2e-2# (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we can determine c, and c2 by solving the equations x(0) = cje0 + c2e(-2)0) = c1(1) + c2(1) = 1, %3D x'(0) = c1(-1)e-0 + c>(-2)e~2x0) = -c1 – 2c2 = 1. (a) Find the values of c and c, by solving the above. (b) Find the solution of the differential equation subject to the specified initial condition by using the above method. i. y" – 3y – 4y = 0; y(0) = 0, y'(0) = 1. ii. y" – 9y' = 0; y(0) = 5, y'(0) = 0. %3D %3D