MATH 315 FALL 2006 TEST 2 KEY
1.
(20 pts.) Consider the differential equation
.
1.
Find the general solution for the equation.
Answer:
characteristic polynomial is
, with roots 0, -1, 2.
The general solution is therefore
2.
Determine the Wronskian for your fundamental solution set.
3.
Determine the solution that satisfies initial conditions
,
,
.
the solution to the linear system is
,
,
.
Final solution:

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2.
(16 pts.) Find the general solution for the differential equation
.
Answer:
characteristic polynomial is
, with roots
, so
A particular solution should have the form
Final solution:
.
3.
(15 pts.) Suppose the general solution to a
order homogeneous equation
is
Determine the general form that would be used with the method of undetermined
coefficients for the solution to the nonhomogeneous equation