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`(4+tan^2(x))y' =sec^2x` Solve the differential equation.

`(4+tan^2(x))y'=sec^2(x)`


`=>y'=(sec^2(x))/(4+tan^2(x))`


`y=int(sec^2(x))/(4+tan^2(x))dx`


Apply integral substitution: `u=tan(x)`


`du=sec^2(x)dx`


`y=int1/(4+u^2)du`


`=int1/(u^2+2^2)du`


Use the standard integral :`int1/(x^2+a^2)dx=1/aarctan(x/a)`


`=1/2arctan(u/2)`


Substitute back u=tan(x) and a constant C to the solution,


`=1/2arctan(tan(x)/2)+C`


`y=1/2arctan(tan(x)/2)+C`

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