4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0 where a3, a2, a1, ay are constants. Use each general solution to determine the constants a3, a2, ɑ1, ao. (a) y(t) = c1 + ©zt + c3 cos(3t) + c4 sin(3t) (b) y(t) = c1 cos(t) + ©2 sin(t) + c3 cos(2t) + c4 sin(2t) %3D

Consider the following equations: (a) y = 3x +7 (b) y + y = 0 (c) y/y= 232 (d) = 84x de (e) a2 + y? = 36 (f) a*/" + 4x*y/ = sin (æº) (g) + æ? = 36t For each of the following questions, answer with a list of letters, such as a,c,d. Which of the equations are: differential equations? linear differential equations? first order differential equations? autonomous differential equations?

b) 2 cos² x + 3 cosx+1 = 0