Question

Question: Solve (2xy + y - tany )dx + (x2 - xtan^2y + sec2y) dy = 0​

Answer 1

Answer: On separating the variables (dividing the equation by \tan  x \tan  y)

⇒

tanx

sec

2

x

​

dx=−

tany

sec

2

y

​

dy

On integrating both sides, we get

∫

tanx

sec

2

x

​

dx=−∫

tany

sec

2

y

​

dy

Put tanx=u⇒sec

2

x.dx=du and tany=v⇒sec

2

y.dy=dv

∴∫

u

du

​

=−∫

v

dv

​

⇒logu=−logv+logc

⇒u=

v

c

​

⇒u.v=c

∴tanx.tany=c

Step-by-step explanation:

Answer 2

Answer:

(2xy+y-tany)dx+(x^2-xtan^2y+sec^2y)dy=0

Step-by-step explanation:

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