Toronto Math Forum
MAT2442019F => MAT244Test & Quizzes => Quiz3 => Topic started by: Yu Qi Huang on October 11, 2019, 02:05:02 PM

Verify that y_1(t) and y_2(t) are solutions of y''  2y' + y = 0 where y_1(t) = e^t and y_2(t) = te^t. Do they constitute a fundamental set?
Solution:
Transforming into characteristic equation the equation becomes:
r^2  2r + 1 = 0
(r  1)^2 = 0
r = 1
Hence y(t) = c_1*e^t + c_2*te^t
w = e^t * (e^t + te^t)  (e^t * te^t)
= (e^t)^2 + e^t(te^t)  (e^t)(te^t)
= (e^t)^2
≠ 0
Hence they do constitute a fundamental set.