s) (cot-1y +x)dy = (1+y^2) doc.
Answers
Answered by
4
For solve the solving the given equation
(1+y
2
)
dx
dy
=cot
−1
y+x
⇒
dx
dy
+x(
1+y
2
−1
)=
1+y
2
cot
−1
y
⇒xe
∫−
1+y
2
dy
=∫e
∫−
1+y
2
dy
1+y
2
cot
−1
y
dy
⇒xe
−tan
−1
y
=e
2
−π
∫e
2
π
e
−tan
−1
y
1+y
2
cot
−1
y
dy
⇒xe
−tan
−1
y
=e
2
−π
∫e
cot
−1
y
1+y
2
cot
−1
y
dy
⇒xe
−tan
−1
y
=−e
2
−π
∫e
t
tdt
⇒xe
−tan
−1
y
=−e
2
−π
[te
t
−e
t
]
⇒xe
−tan
−1
y
=e
2
−π
[cot
−1
y−1]e
cot
−1
y
⇒xe
−tan
−1
y
=e
2
−π
+C
x=1+Ce
tan
−1
y
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