Solve the following differential equations: `(x+tany)dy=sin2ydx`

Explanation

`(x+tan y) d y=sin 2 y d x `
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Rightarrow fracd xd y=fracx+tan ysin 2 y `
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Rightarrow fracd xd y=fracxsin 2 y+fractan ysin 2 y `
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Rightarrow fracd xd y-cosec 2 y cdot x=frac12 sec ^2 y (because sin x=frac1cosec x ; tan x=fracsin xcos x ; sin 2 x=2 sin x cos x) `


since this is in the form of `fracdxdy+Rx=S`
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where, R=-cosec 2 y and S=frac12 sec ^2 y`
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