Determine which of the following sets of vectors is a basis for the solution space to the differential equation x 2 y ″ − 3 x y ′ + 4 y = 0 on the interval ( 0 , ∞ ) . S 1 = { x 2 } , S 2 = { x 2 , x 2 ln x } , S 3 = { 2 x 2 , 3 x 2 ln x } , S 4 = { x 2 ( 2 + 3 ln x ) , x 2 ( 2 − 3 ln x ) } .
Determine which of the following sets of vectors is a basis for the solution space to the differential equation x 2 y ″ − 3 x y ′ + 4 y = 0 on the interval ( 0 , ∞ ) . S 1 = { x 2 } , S 2 = { x 2 , x 2 ln x } , S 3 = { 2 x 2 , 3 x 2 ln x } , S 4 = { x 2 ( 2 + 3 ln x ) , x 2 ( 2 − 3 ln x ) } .
Solution Summary: The author explains that the vectors S_2,
Determine which of the following sets of vectors is a basis for the solution space to the differential equation
x
2
y
″
−
3
x
y
′
+
4
y
=
0
on the interval
(
0
,
∞
)
.
S
1
=
{
x
2
}
,
S
2
=
{
x
2
,
x
2
ln
x
}
,
S
3
=
{
2
x
2
,
3
x
2
ln
x
}
,
S
4
=
{
x
2
(
2
+
3
ln
x
)
,
x
2
(
2
−
3
ln
x
)
}
.
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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