Consider the equation ay__ + by_ + cy = 0, (35) where a, b, and c are constants with a
Chapter 7, Problem 21(choose chapter or problem)
Consider the equation ay__ + by_ + cy = 0, (35) where a, b, and c are constants with a _= 0. In Chapter 3 it was shown that the general solution depended on the roots of the characteristic equation ar2 + br + c = 0. (36) a. Transform equation (35) into a system of first-order equations by letting x1 = y, x2 = y_. Find the system of equations x_ = Ax satisfied by x = _x1 x2 _. b. Find the equation that determines the eigenvalues of the coefficient matrix A in part a. Note that this equation is just the characteristic equation (36) of equation (35). 2
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