Solve the differential equation: `x cos^2y dx=y cos^2xdy`

Explanation

`x cos ^{2} y d x=y cos ^{2} x d y `


Separate variables of equation


`Rightarrow frac{x}{cos ^{2} x} d x=frac{y}{cos ^{2} y} d y`


`Rightarrow x sec ^{2} x d x=y sec ^{2} y d y`


Integrate both sides of equation by part method


`Rightarrow x int sec ^{2} x d x-int{frac{d}{d x}(x) int sec ^{2} x d x} d x=y int sec ^{2} y d y-int{frac{d}{d y}(y) int sec ^{2} y d y} d y `


`Rightarrow x tan x-int tan x d x=y tan y-int tan y d y`


Use identity:` \int \tan x d x=\log |\sec x|`


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