1. Evaluate sin(x-3) + [ex sin (2x-1)]. 2. 3. 4. 5. Find the general solution of the linear, first-order differential equation dx 1 + dt - x = 6t t using an integrating factor. Find the general solution of the linear, homogeneous, second-order differential equation dy dx dy -6y = 0. dx Find the general solution of the linear, nonhomogeneous, second-order differential equation dx dt -2 + x = e' . dx dt Solve the initial-value problem d y +4y = 6 sin 4x, y(0) = 0, y'(0) = 1. dx