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)'
(b) Solve the following Cauchy-Euler system:
(t > 0)
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