Answers to Gateway #13

Sec. 3.4 (BDH)

e^t * ( 2cos(3t)-sin(3t) )
      ( cos(3t)		 )

e^t * ( cos(3t)+2sin(3t) )
      ( sin(3t)		 )

#6a The eigenvalues are -0.50000000000000 + 1.93649167310371i and -0.50000000000000 - 1.93649167310371i.

#6b Since they have negative real part, the origin is a spiral sink.

#6d Solutions go clockwise.

#12a

k1*e^(-0.5t) * ( a1*cos(wt) - b1*sin(wt) )
	       ( -b2*sin(wt)		 )

+ k2 *e^(-0.5t) * ( b1*cos(wt) + a1*sin(wt) )
		  ( b2*cos(wt)		    )

where

	a1 = 0.68465319688146, b1 = - 0.17677669529664, 
	b2 = 0.70710678118655 and w = 1.93649167310371.

#12b k1 = -1.09544511501032, k2 = sqrt(2) Note: These answers will vary depending on the choice of eigenvectors.

Last modified: Thur Jan 30 16:44:48 1997