If yp = te-6t cos 7t solves a second order equation Ay" + By' + cy=f, what does that tell you about B, C and f? (Mechanical system)

Non Homogeneous LDE solve:(D2  +  D  -  2)y  =  2x  -  40 cos 2x

5 (C) A student asks how you prove the other 2 versions of the Law of Cosines found in equations (5.9) and (5.10). How do you do it? b² + c² – a² cos A = (5.9) 2bc a² + c2 – b2 Cos B = (5.10) 2ac

A pendulum on a rigid rod oscillates according to the equation 8²0 Ət² + sin 0 = 0, where is the angle of the pendulum from the vertical. 1. Show that 0 = 0 (the pendulum hanging straight down) and 0 = (the pendulum balanced vertically up) are possible equilibrium solutions of the equation.

please solve it on paper   The second pic is the answers from the answer key