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4.3.2
Linear ode with non-constant coefficients
A
(
x
)
y
′
′
+
B
(
x
)
y
′
+
C
(
x
)
y
=
f
(
x
)
4.3.2.1
Collection of special transformations
4.3.2.2
Euler ode
x
2
y
′
′
+
x
y
′
+
y
=
f
(
x
)
4.3.2.3
Kovacic type
4.3.2.4
Method of conversion to first order Riccati
4.3.2.5
Airy ode
y
′
′
±
k
x
y
=
0
or
y
′
′
+
b
y
′
±
k
x
y
=
0
4.3.2.6
Solved using series method
4.3.2.7
Reduction of order
4.3.2.8
Transformation to a constant coefficient ODE methods
4.3.2.9
Exact linear second order ode
p
2
(
x
)
y
′
′
+
p
1
(
x
)
y
′
+
p
0
(
x
)
y
=
f
(
x
)
4.3.2.10
Linear second order not exact but solved by finding an integrating factor.
4.3.2.11
Linear second order not exact but solved by finding an M integrating factor.
4.3.2.12
Solved using Lagrange adjoint equation method.
4.3.2.13
Solved By transformation on
B
(
x
)
for ODE
A
y
′
′
(
x
)
+
B
y
′
(
x
)
+
C
(
x
)
y
(
x
)
=
0
4.3.2.14
Bessel type ode
x
2
y
′
′
+
x
y
′
+
(
x
2
−
n
2
)
y
=
f
(
x
)
4.3.2.15
Bessel form A type ode
a
y
′
′
+
b
y
′
+
(
c
e
r
x
−
m
)
y
=
f
(
x
)
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