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प्रश्न
For the differential equation, find the general solution:
`dy/dx = (1 - cos x)/(1+cos x)`
योग
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उत्तर
`dy/dx = (1 - cos x)/(1 + cos x) = (1 - 1 + 2 sin^2 x/2)/(1 + 2 cos^2 x/2 - 1)`
`dy/dx = (sin^2 x/2)/(cos^2 x/2) = tan^2 x/2`
`dy = tan^2 x/2 dx`
On integrating
`int 1. dy = int tan^2 x/2 dx`
`int 1. dy = int (sec^2 x/2 - 1) dx`
`y = 2 tan x/2 - x + C`
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