In Problems 27 through 31 , verify that y ( t ) satisfies the given differential equation. Then determine a value of the constant C so that y ( t ) satisfies the given initial condition. t y ' + ( t + 1 ) y = t ; y ( t ) = ( 1 − 1 / t ) + C e − t / t , y ( ln 2 ) = 1
In Problems 27 through 31 , verify that y ( t ) satisfies the given differential equation. Then determine a value of the constant C so that y ( t ) satisfies the given initial condition. t y ' + ( t + 1 ) y = t ; y ( t ) = ( 1 − 1 / t ) + C e − t / t , y ( ln 2 ) = 1
In Problems
27
through
31
, verify that
y
(
t
)
satisfies the given differential equation. Then determine a value of the constant
C
so that
y
(
t
)
satisfies the given initial condition.
t
y
'
+
(
t
+
1
)
y
=
t
;
y
(
t
)
=
(
1
−
1
/
t
)
+
C
e
−
t
/
t
,
y
(
ln
2
)
=
1
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