AMATH350 Lecture Notes - Lecture 8: Market Clearing, Economic Equilibrium

• School: University of Waterloo
• Department: Applied Mathematics
• Course: AMATH350
• Professor: Mohamad Alwan

Document Summary

6y = 0, y1 = x2 y1 = x1/2 ln x yp(x) = u(x)ex: use the variation of parameters method to nd the particular solutions for the following des. 2y + 2y = ex tan x (b) y . 2ex ex + e x: give the form of the particular solution which you would use in the method of undetermined. Coe cients for the de. (do not try to solve for the coe cients). (d3 + 2d2 + 2d)[y] = x2 + 3xe x + xe x cos(x) 2: show that the set of following functions are linearly independent. 2 (cid:19) e2x: consider the following homogeneous systems of des (a) (b) (c) dy1 dt dx dt. ~y = ~y(t) = (cid:18) y1(t) (a) find the eigenvalues i and the corresponding eigenvectors ~vi of the matrix a of each system. (b) find the linearly independent solutions ~yi(t) = e it~vi. Then, nd the general solution of each system. to be continued