Find the general solution of each of the following differential equations:
`(cosx)(dy)/(dx)+cos2x = cos 3x`

Answer

`y=sin 2x -2 sinx -x +log |sec x +tan x |+C`

Explanation

`(dy)/(dx)=(cos3x-cos 2x)/(cosx)=((4cos^(3)x-3cosx)-(2cos^(2)x-1))/(cosx)`
`rArr (dy)/(dx)=4cos^(2)x-2cosx-3+secx`
` rArr (dy)/(dx) =(4(1+cos2x))/(2)-2cosx-3 +secx =2 cos 2x -2cosx -1 +sec x.`