Question

A system of differential equations having the form t(~x)' = A ~x, where A is a...

A system of differential equations having the form
t(~x)' = A ~x,
where A is a matrix with constant entries, is known as a Cauchy-Euler system.

(a) Suppose λ is an eigenvalue of A and ~ v is an eigenvector corresponding to λ. Show that the function

x(t) = t^λ (v)

is a solution to the Cauchy-Euler system t(x)' = A(x).
(b) Solve the following Cauchy-Euler system:
t(x)' =

3 -2
2 -2

(x)

(t > 0)

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