For Problems 13 − 16 , determine terms up to and including x 5 in two linearly independent power series solutions of the given differential equation. State the radius of convergence of the series solutions. y ′ ′ − e x y = 0 . [ Hint: e x = 1 + x + 1 2 ! x 2 + 1 3 ! x 3 + … .]
For Problems 13 − 16 , determine terms up to and including x 5 in two linearly independent power series solutions of the given differential equation. State the radius of convergence of the series solutions. y ′ ′ − e x y = 0 . [ Hint: e x = 1 + x + 1 2 ! x 2 + 1 3 ! x 3 + … .]
Solution Summary: The author determines the terms up to and including x5 in two linearly independent power series solutions of the given differential equation.
For Problems
13
−
16
, determine terms up to and including
x
5
in two linearly independent power series solutions of the given differential equation. State the radius of convergence of the series solutions.
y
′
′
−
e
x
y
=
0
. [Hint:
e
x
=
1
+
x
+
1
2
!
x
2
+
1
3
!
x
3
+
…
.]
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