Question

f(t)=e^( λt )cos(μt),g(t)=e ^(λt) sin(μt),μ≠0
are those functions linearly independent

Answer 1

gonna have to play with a wronskian it looks like

Answer 2

http://www.sosmath.com/diffeq/second/linearind/linearind.html

Answer 3

http://www.wolframalpha.com/input/?i=wronskian++of+e^%28+%CE%BBt+%29cos%28%CE%BCt%29%2Ce+^%28%CE%BBt%29+sin%28%CE%BCt%29

Answer 4

The above shows that the Wronskian is never zero, so they are linearly independent