(1) will write us of the following form
\(\dfrac{dy}{dx}+y^2\sin x=0\\ \\\)
(2) [do not it need explanation]
\(\dfrac{dy}{dx}=-y^2\sin x\\ \\\)
(3) Left place variable "y" and right place, variable "x" like this
\(\dfrac{dy}{y^2}=-\sin x\, dx\\ \\\)
(4) Integrate both members
\(\displaystyle
\int \dfrac{dy}{y^2}=\int-\sin x\, dx\\ \\\)
(5) Solve us the integrals
\(-\dfrac{1}{y}= \cos x+C\)
(6) Isolate variable "y"
\(\boxed{y=-\dfrac{1}{\cos x+C}}\)
C: any cosntant
