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Sat 24 Sep, 2005 09:17 pm
Hi all! Suppose I'm solving a 2 by 2 linear constant coefficient ODE system:
dx/dt = ax + by
dy/dt = cx + dy
and from the matrix with a, b, c, and d I get two eigenvalues:
lamda_1 = 0, lambda_2 = 5
Well, then I guess my question really is:
What will be the general form of the solution?
It can't be
X(t) = c_1 * e^(lambda_1)*t*v_1 + c_2 * e^(lamda_2)*t*v_2 because we need at least two independent solutions to span the entire solution space of the system.
Please advise. Thanks!
What's wrong people? Too hard???
any other way of asking that question... it appears that the terminology we use for algebra is different here than were u are...
Milfmaster9 wrote:any other way of asking that question... it appears that the terminology we use for algebra is different here than were u are...
OK. Well, put simply, what is the solution of a Linear, 2 by 2, constant coefficient ODE system, when the eigenvalues of its associated matrix are 0 and 5?
Note that one of the eigenvalues of the matrix
Code:
A= a b
c d
equals zero, then the matrix A is degenerate and the differential equation reduces to the one of the form
x' = Kx + L
(K, L : constants; prime means the derivative with respect to t)
and you can solve with respect to x in the above form of the equation.
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