Question

Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M, and verify that the equation Ny + M c. (2/20) Use the particular integrating factor with u(0)= 1 to compute the functions N 0 is indeed exact. aN(t,y) = 3 M(t,y) = d. (6/20) Find a potential function , such that any solution y to the differential equation in (c) satisfies (t, y) c. (Collect in c all constants terms function .) (t,y)

Answer 1

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