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Mathematics
Mathematics
Problem
Find the solution to the differential equation
(
x
+
1
x
)
d
y
d
x
+
2
y
=
2
(
x
2
+
1
)
2
\left(x + \frac{1}{x}\right) \frac{dy}{dx} + 2y = 2(x^2 + 1)^2
(
x
+
x
1
)
d
x
d
y
+
2
y
=
2
(
x
2
+
1
)
2
giving
y
y
y
in terms of
x
x
x
. a. Find the general solution. b. Find the particular solution satisfying the condition that
y
=
1
y = 1
y
=
1
at
x
=
1
x = 1
x
=
1
.
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