W8 1 A Use The Eigenvalue Eigenvector Method With Complex Eigenvalues To Solve The First Order System Initial Value 1 (34.72 KiB) Viewed 22 times
W8 1 A Use The Eigenvalue Eigenvector Method With Complex Eigenvalues To Solve The First Order System Initial Value 2 (11.18 KiB) Viewed 22 times
w8.1 (a) Use the eigenvalue-eigenvector method (with complex eigenvalues) to solve the first order system initial value problem which is equivalent to the second order differential IVP from Wednesday June 28 notes. This is the reverse procedure from Wednesday, when we use the solutions from the equivalent second order DE IVP to deduce the solution to the first order IVP. Of course, your answer here should be consistent with our work there. [zi(t)] [₂(t)] 21 [1(0)] [-28] - [4] = 2(0) (b) Verify that the first component r₁(t) of your solution to part a is indeed the solution r(t) to the IVP we started with, a" (t)+2é! (t)+5(t)=0 x(0) = 4 x' (0) = -4
C: For the first order system in w8.1 is the origin a stable or unstable equilibrium point? What is the precise classification based on the description of isolated critical points in section 5.3?
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