Question

(1 point) Consider the Initial Value Problem -5 dx dt X x(0) (a) Find the eigenvalues and eigenvectors for the coefficient matrix A = and 2 -- 1 333 (b) Find the solution to the initial value problem. Give your solution in real form Use the phase plotter pplane9.m in MATLAB to help you describe the trajectory Spiral, spiraling inward in the counterclockwise direction 1. Describe the trajectory

Answer 1

da -5 -1 [i]. [core 21- -5 AL S- 1*=5] des fonds). * (151)45-1951 (5+1) 7150 5+1 = d= -5t ti di= -5- 12. -5 t Eigen vectors -5-Å [17] [A-d IIV - for di [A-d, I] E Vi + V2 = ivi d N =-1t V2 = 0 Vert t tolce tu! 3-13

for 12-5+ 1-5 -1 al -1,5 :"]=[:] let V2=t V-IV = 0 taket! h = ) X, LH) en 5-8) * **** ( 09:4j+(3+) [:) 56 é Sin H Ali cosit) est concet) fiest girlt) والبيع - CF فرز 1 teel center suf = 616 * * * * * L-shi] ام رين - att) est F-ci sint + C2 cost) cost - C₂ sint) 190) - 2 ot-C2 CA 1 C2 = 7 (1=5 X- -54 -5 sint + 7-Coft) Sint) + 5 00318)
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