Question

Problem 7. (1 point) a. Find the most genera reat valued solution to the inear system of diferential equations t' = [": -); x1 (1) = C C + C2 x2 (1) u b. In the phase plane, this system is best described as a source / unstable node sink / stable node O saddle center point / ellipses O spiral source spiral sink none of these

Answer 1

Solution: (a) given that 113 6 bet 5] 5 6 we find eigenvalues of A So we need det (A-AI)=0 to solve T |-9-1 6 54 (9-x) (5-1) + 48=0 " -45+90-5 4+1 +48=0 T 12 A + 4 +3=0 12 TI +2+3 8+3 = 0 A (A41)+ 3 (4+1) = 0 T darl,-3 tunc eigenvalues of A are da-3,1 Now, we find ergenuertes corresponding to each eigenvalues. So when darz. Then we need to nolue (A-AI) U=0 CA+31) U=0

1 6 R, Ritra ETIQ)(3) 18:1()=(8) JC)-(3) y ܕܐ ܕܹ… ܕ 3 4 =) 3x+4y=0 9) 4 y = -34 y = -3 4 N Let s=4 Then y=3 Hunu, ( 4 ) in an eigenwechy Now, when -- So, we need to solve A-11) = 0 (A +I) U=0 -) 8 -8 6 a j)-13) Paper B, att :](31:18 R, IR Lou!I (3)=79)