Math, asked by ardrachikkuown0eb, 6 months ago

s) (cot-1y +x)dy = (1+y^2) doc.​

Answers

Answered by shinchen08
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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