Summary: USING COMPLEX NUMBERS TO FIND PARTICULAR
SOLUTIONS
MATH 2574H, SPRING 2012
UNIVERSITY OF MINNESOTA
INSTRUCTOR: PROF. GREG ANDERSON
Problem
Find a particular solution of y + y = 2 cos(t) using complex numbers.
Solution using complex numbers
I will use the operator factorization method and Euler's formula. I won't include
any constants of integration because I am only looking for a particular solution.
y + y = 2 cos(t)
(D2
+ 1)y = eit
+ e-it
(D + i)(D - i)y = eit
+ e-it
Deit
(D - i)y = e2it
+ 1
eit

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

Collections: Mathematics