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Math 2214 Friday, November 10
Third Test. Answer All Problems.
Please Give Explanations For Your Answers
1. Find the general solution of the differential equation y
(4)
+2y
primeprime
+y = 0. (10 points)
2. Write the linear differential equation y
primeprime
+ty
prime
+t
2
y = t
3
in the form y
prime
= P(t)y+g(t),
where P isa2×2 matrix. Identify the matrix function P(t) and the vector function
g(t). (10 points)
3. Find the general solution of the system of differential equations x
prime
= 2x?y, y
prime
= x.
(15 points)
4. Let A =
parenleftbigg
1 ?1
2 ?1
parenrightbigg
and g =
parenleftbigg
e
t
0
parenrightbigg
. Find the general solution of the system of differen-
tial equations y
prime
= Ay+g by the method of undetermined coefficients. (15 points)
Math 2214 Friday, November 10
Solutions to Third Test
1. The characteristic equation is r
4
+2r
2
+1 = 0, which is (r
2
+1)
2
= 0. Since the roots
of r
2
+1 are ±i, we see that the roots of (r
2
+1)
2
are ±...

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