Consider the second-order equation d2 y dt2 + p dy dt + qy
Chapter , Problem 19(choose chapter or problem)
Consider the second-order equation
\(\frac{d^{2} y}{d t^{2}}+p \frac{d y}{d t}+q y=0\),
where p and q are positive.
(a) Convert this equation into a first-order, linear system.
(b) Compute the characteristic polynomial of the system.
(c) Find the eigenvalues.
(d) Under what conditions on p and q are the eigenvalues two distinct real numbers?
(e) Verify that the eigenvalues are negative if they are real numbers.
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