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Unformatted text preview: 3xy 0 3y = 0.
c) Use the variation of parameters y0 = 3to solve the equation x2 y 00 +3xy 0
and method .
3y = .
5. Consider the DE y = Ay where
0 of the system y0 = Ay + F(x), where
2. Find the general solution 5
(a) Show that A has one eigenvalue of multiplicity 2 that has two linearly
independent A =
eigenvectors. 2 , and Fthe general 0
Hence give (x) =
solution of the DE.
(b) Write the DE in component form, solve the resulting equations and
compare your answer with part (a).
6. Find the general solution the equation 0 ( = Ay + f x) where
3. Find the general solution of of the systemxy t) = Ax+F,(where A =
, and F(x) =
and f (t) =
4 + 2/t 1 7. Consider a commodity with constant supply S = 50 and demand curve
4. Consider a commodity with constant supply S = 50. Suppose the demand
whose derivative is given by
curve has derivative
dD 2D 5p + 10
dtdt = 2D 5p + 10
where D is the demand and is the price. The rate of of increase of price
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- Fall '12