Solve: `(dy)/(dx)+ytanx=2x+x^2tanxdot`

Explanation

`frac{d y}{d x}+tan x cdot y=2 x+x^{2} tan x`


I.F. `=e{ln (sec x)=sec x}`


`y sec x=int(2 x+x^{2} tan x) sec x d x+c=I_{1}+c`


`y sec x=int 2 x sec x d x+int x^{2} sec x tan x d x`


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


`y sec x=x^{2} sec x+c`


`y=x^{2}+{ccos} x`