Question

Solution of the differential equation tany sec²xdx + tanx sec²ydy = 0 is ______.

Options

• tanx + tany = k

• tanx – tany = k

• `tanx/tany` = k

• tanx . tany = k

Answer 1

Solution of the differential equation tany sec²xdx + tanx sec²ydy = 0 is tanx . tany = k.

Explanation:

The given differential equation is tan y sec²x dx + tan x sec²y dy = 0

⇒ tan x sec²y dy = – tan y sec²x dx

⇒ `(sec^2y)/tany * "d"y = (-sec^2x)/tanx * "d"x`

Integrating both sides, we get

⇒ `int (sec^2y)/tany "d"y = int (-sec^2x)/tanx  "d"x`

⇒ `log |tan y| = - log |tan x| + log "c"`

⇒ `log |tan y| + log |tan x| = log "c"`