Question

(4+x^2)dy +4dx=0

Answer 1

$$dy=-\dfrac{4}{4+x^2}dx$$

Integrate

$$\int dy=-\int\dfrac{4}{4+x^2}dx$$

$$\int\dfrac{4}{4+x^2}dx=\int\dfrac{1}{1+(x/2)^2}dx=2\arctan (x/2)+C$$

Then

$$y=-2\arctan(x/2)+C$$