Find the general solution of the differential equations `sec^2xtany dx+sec^2ytanx dy=0`

Answer

`tanx * tany= c`

Explanation

We have,

`sec ^{2} x tan y * d x+ sec ^{2} y tan x* d y=0`

On separating the variables (dividing the equation by `tanx tany` ),


`rArr frac{ sec ^{2} x}{ tan x} d x=- frac{ sec ^{2} y}{ tan y} d y`


On integrating both sides, we get,


`int frac{ sec ^{2} x}{ tan x} d x=- int frac{ sec ^{2} y}{ tan y} dy`


Put `tan x=u rArr sec ^{2} x *d x=d u `
and ` tan y=v rArr sec ^{2} y *dy=d v `


`therefore int frac{du}{u}=- int frac{dv}{v}`


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