In each of Problems 22 through 27, verify that the given functions y 1 and y 2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. In Problems 26 and 27, g is an arbitrary continuous function. ( 1 − x ) y ″ + x y ' − y = g ( x ) , 0 < x < 1 ; y 1 ( x ) = e x , y 2 ( x ) = x
In each of Problems 22 through 27, verify that the given functions y 1 and y 2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. In Problems 26 and 27, g is an arbitrary continuous function. ( 1 − x ) y ″ + x y ' − y = g ( x ) , 0 < x < 1 ; y 1 ( x ) = e x , y 2 ( x ) = x
In each of Problems 22 through 27, verify that the given functions
y
1
and
y
2
satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. In Problems 26 and 27,
g
is an arbitrary continuous function.
(
1
−
x
)
y
″
+
x
y
'
−
y
=
g
(
x
)
,
0
<
x
<
1
;
y
1
(
x
)
=
e
x
,
y
2
(
x
)
=
x
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