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1
Frobenius series. Indicial equation with repeated root
1.1
Example 1. homogeneous ode
x
2
y
′
′
(
x
)
+
x
y
′
(
x
)
+
x
2
y
(
x
)
=
0
1.2
Example 2. inhomogeneous ode example
x
2
y
′
′
(
x
)
+
x
y
′
(
x
)
+
x
2
y
(
x
)
=
sin
(
x
)
1.3
Example 3. homogeneous ode example
(
e
x
−
1
)
y
′
′
(
x
)
+
e
x
y
′
(
x
)
+
y
(
x
)
=
0
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