Homework 5; Due Thursday March 5, 2009




1.  Give a basis for the real solutions of y''' + 2y'' + 4 y' + 8y = 0.





2.  Give a basis for the vector space of real solutions of the equation 


                y'' + 8y' + 7y = 0

consisting of of functions f_1 and f_2 such that

             f_1(0) = 1; f_1'(0) =  0;

             f_2(0) = 0; f_2'(0) = 1.

(Note f_2  is the Tex notation for f subscript 2; f^2 is the Tex notation
for f squared. Mathematicians all understand this typed shorthand. It is
very convenient).


3.  Find the general solution to the equation


             y'' + 3y' + 2y = 3 + e^(-3t).



4.  Find the general solution to the equation


             y'' + 2y' + 2y  = sin (3t).




5. Use the material in section 3.9 to apply formula (13) to the case of
the forced vibration

           y'' +  y =   sin (1.2 t).

What is the general solution?  What is the period of the amplitude modulation?
Look back at problem 4 of last week's homework. Does the graph make sense now?