ENGR 213 Lecture 9: 3.3_Homogeneous_Linear_Equations_with_Constant_Coefficients

• School: Concordia University
• Department: Engineering
• Course: ENGR 213
• Professor: Georgios Vatistas

Document Summary

Special case of a second-order equation ay + by + cy = 0 y = emx y = memx y = m e2 mx. 2 mx am e + mx e bme +mx. 2 (am + am +2 ce =mx bm + c) = 0 bm + c = 0. Case 1: distinct real roots m1 = m2 y = c e. Case 2: repeated real roots m =1 m2 m x1 y = c e. 1 i =2 "1 ( +i )c c e2 ( "i )x. In practice, we prefer to work with real functions instead of complex exponentials, use euler"s formula e =i x cos x + i sin x and e e =i cos + i sin . X sin x y = c e c e. X c sin x) y = e (c cos x + 5m " 3 = (2m + 1)(m " 3), m =1 " , m =