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Mathematics
Problem
Find the general solution to the differential equation
x
2
d
y
d
x
+
2
x
y
=
2
x
+
1
x^2 \frac{dy}{dx} + 2xy = 2x + 1
x
2
d
x
d
y
+
2
x
y
=
2
x
+
1
b. Find the three particular solutions which pass through the points with coordinates
(
−
1
2
,
0
)
(-\frac{1}{2}, 0)
(
−
2
1
,
0
)
,
(
−
1
2
,
3
)
(-\frac{1}{2}, 3)
(
−
2
1
,
3
)
and
(
−
1
2
,
19
)
(-\frac{1}{2}, 19)
(
−
2
1
,
19
)
respectively and sketch their solution curves for
x
<
0
x < 0
x
<
0
.
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