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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
Solution
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"`
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