Unformatted text preview: 3xy 0 3y = 0.
14
c) Use the variation of parameters y0 = 3to solve the equation x2 y 00 +3xy 0
A=
and method .
47
2
1
3y = .
x
5. Consider the DE y = Ay where
50
A=
.
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
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4xe x
.
independent A =
eigenvectors. 2 , and Fthe general 0
Hence give (x) =
solution of the DE.
1
(b) Write the DE in component form, solve the resulting equations and
compare your answer with part (a).
✓
◆
42
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 =
2
1
✓
◆2 1
4xe x
1=
A/t
, and F(x) =
.
and f (t) =
.
2
0
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
dD 2D 5p + 10
=
dtdt = 2D 5p + 10
where D is the demand and is the price. The rate of of increase of price
where D...
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 Fall '12
 DavidHamsworth
 Boundary value problem, general solution

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