Question

Find the general solution of the differential equation `tan y * dy/dx = sin(x + y) - sin(x - y)`.

Answer 1

`tan y dy/dx = sin(x + y) - sin(x - y)`

∴ `siny/cosy * dy/dx = 2cosx*siny`

∴ `1/cosy * dy = 2 cos x  dx`

Integrating both sides,

`int sec y  dy = 2int cos x  dx`

∴ log |sec y + tan y| = 2 sin x + c