# Thread: write the general solution...

1. ## write the general solution...

the eigenvalues for X'=AX as [3-i,3+i,-3] with the eigenvectors of [1,(-5+7i)/2, (5-3i)/2] and [1, (-5-7i)/2, (5+3i)/2 ]

im supposed to write the general solution using only real coefficients...

im not sure how to do this problem....

a little help would be nice..

2. Use

$e^{(3+i)t}+e^{(3-i)t}=2e^{3t}\cos t$

$e^{(3+i)t}-e^{(3-i)t}=2ie^{3t}\sin t$

3. sorry i left out one vector...

[1,0,-1/3]

this is what i know about the problem thus far....

this is what i know so far....

i know lambda will equal to 3+i

i also know the formula is X1=C1[B1*cos t - B2*sin t ]e^3t

X2= C2[B2*cos t + B1*sin t]e^3t...

X3, im not so sure about....

4. If $v_1,v_2,v_3$ are the corresponding eigenvectors associated to $3,3+i,3-i$ respectively, write $X=C_1e^{3t}v_1+C_2e^{(3+i)t}v_2+C_3e^{(3-i)t}v_3$ and use the equalities of answer #2.