Let U1 and U2 be two linearly independent solutions of the second-order linear differential equation d²u fu + dx² 2 - y' Let w= uz/u1. Let y=-2u₁/u₁. ,2 0, f = f(x). 2 = f. (iii) Show that w"/w' = - 2u₁/u₁, and deduce that w satisfies the equation 2 1 ()'. () - () - 2 = f.

Find a differential equation for y=c1e^9t +c2e^-4t. O y"+5y +16y=0 O y"-5y'-16y=0 Oy"+5y'+36y=0 Oy"-5y'-36y=0

For the differential equation y' = 2y - x, draw line segments representing the slope field at the points (1, 2), (1, 1), (2, 2), and (2, 1).