coursehero4.pdf - 4 System of ODEs Exercise 4.1 a > B =[1.2...

This preview shows page 1 - 4 out of 6 pages.

4: System of ODEs Exercise 4.1 a) >> B = [1.2 2.5; 4 0.7] B = 1.2000 2.5000 4.0000 0.7000 b) >> [eigvec, eigval] = eig(B) eigvec = 0.6501 -0.5899 0.7599 0.8075 eigval = 4.1221 0 0 -2.2221 Exercise 4.2 a) >> A = [3 4 ; -1 -2] A = 3 4 -1 -2 b) >> [eigvec, eigval] = eig(A) eigvec = 0.9701 -0.7071 -0.2425 0.7071 eigval = 2 0 0 -1 c) v(t) = C 1* e 2t [0.9701; -0.2425] + C 2 *e -t [-0.7071; 0.7071] As t gets larger, the term with e 2t gets larger, while the term with e -t gets smaller, meaning the system ultimately goes to infinity as t increases.
d) As shown in the graph, the solutions to the graphed system of differential equations approach either infinity or zero. Exercise 4.3 a) >> A = [2.7 -1; 4.1 3.7] A = 2.7000 -1.0000 4.1000 3.7000 >> [eigvec, eigval] = eig(A) eigvec = -0.1093 + 0.4291i -0.1093 - 0.4291i 0.8966 + 0.0000i 0.8966 + 0.0000i eigval = 3.2000 + 1.9621i 0.0000 + 0.0000i 0.0000 + 0.0000i 3.2000 - 1.9621i b) x'=2.7x-y y'=4.1x+3.7y
Exercise 4.4 a) >> A = [1.25, -0.97, 4.6; -2.6, -5.2, -0.31; 1.18, -10.3, 1.12] A = 1.2500 -0.9700 4.6000 -2.6000 -5.2000 -0.3100 1.1800 -10.3000 1.1200 >> [eigvec, eigval] = eig(A) eigvec = 0.7351 + 0.0000i 0.4490 + 0.2591i 0.4490 - 0.2591i -0.1961 + 0.0000i -0.3375 + 0.2242i -0.3375 - 0.2242i 0.6490 + 0.0000i -0.7530 + 0.0000i -0.7530 + 0.0000i eigval = 5.5698 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -4.1999 + 2.6606i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -4.1999 - 2.6606i

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture