For Problems 45–50, verify that the given function is a solution to the given differential equation. In these problems, c 1 and c 2 are arbitrary constants. y ( x ) = c 1 e x + c 2 e − x ( 1 + 2 x + 2 x 2 ) , x y ″ − 2 y ′ + ( 2 − x ) y = 0 , x > 0 .
For Problems 45–50, verify that the given function is a solution to the given differential equation. In these problems, c 1 and c 2 are arbitrary constants. y ( x ) = c 1 e x + c 2 e − x ( 1 + 2 x + 2 x 2 ) , x y ″ − 2 y ′ + ( 2 − x ) y = 0 , x > 0 .
Solution Summary: The author explains how the equation y(x) is the solution to the differential equation.
For Problems 45–50, verify that the given function is a solution to the given differential equation. In these problems,
c
1
and
c
2
are arbitrary constants.
y
(
x
)
=
c
1
e
x
+
c
2
e
−
x
(
1
+
2
x
+
2
x
2
)
,
x
y
″
−
2
y
′
+
(
2
−
x
)
y
=
0
,
x
>
0
.
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