Math 20D
Solutions
Friday 5/4/2007
1. (a) second order linear
(b) first order linear
(c) first order nonlinear
(d) second order nonlinear
(e) first order linear
2. Compute
y
0
1
y
2

y
1
y
0
2
(the Wronskian) and see if it is nonzero at some point.
Alternatively verify that one function is not a constant multiple of the other.
3. There are 3:
y
=

1 is stable,
y
= 0 is unstable and
y
= +1 is stable.
Your answer should show how you got these results.
4. (a) The answer is 2 sin(3
t
).
The general solution is
c
1
sin(3
t
) +
c
2
cos(3
t
).
By the
initial conditions,
c
1
= 2 and
c
2
= 0.
Your solution should show how the general solution was found.
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 Fall '06
 Mohanty
 Math, Differential Equations, Equations, Derivative, Trigraph, Constant of integration, general solution

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