Question

The differential equation

+ tan =
2
sec is_ _ _ _ _

Answer 1

Answer:

tanysec

2

xdx+tanxsec

2

ydy=0

⇒tanysec

2

xdx=−tanxsec

2

ydy

⇒

tanx

sec

2

x

dx=−

tany

sec

2

y

dy

⇒∫

tanx

sec

2

x

dx=∫−

tany

sec

2

y

dy

let tanx be equal to b and tany equal to a

⇒∫

b

dx

=−∫

a

dy

⇒lnb=−lna+k

⇒lnab=k

⇒lntanxtany=k

⇒tanxtany=k