Example 28 Solve the differential equation
(tan–1y  – x) dy = (1 + y2) dx Solution The given differential equation can be written as
2
1
dx
x
dy
y
+
+
 =
1
2
1tan
y
y
−
+ (1)
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DIFFERENTIAL EQUATIONS
419
Now (1) is a linear differential equation of the form 
1P
dx
dy +
 x = Q1,
where,
P1 =
112
+y
 and 
1
1
2
tan
Q
1
y
y
−
=
+ Therefore,
I