Problems Show that the set of all solutions to the nonhomogeneous differential equation y ″ + a 1 y ′ + a 2 y = F ( x ) , Where F ( x ) is nonzero on an interval I , is not a subspace of C 2 ( I ) .
Problems Show that the set of all solutions to the nonhomogeneous differential equation y ″ + a 1 y ′ + a 2 y = F ( x ) , Where F ( x ) is nonzero on an interval I , is not a subspace of C 2 ( I ) .
Solution Summary: The author explains that the set of all the solution to the given differential equation is not a subspace of C2(I).
Show that the set of all solutions to the nonhomogeneous differential equation
y
″
+
a
1
y
′
+
a
2
y
=
F
(
x
)
,
Where
F
(
x
)
is nonzero on an interval I, is not a subspace of
C
2
(
I
)
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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