Question

Solve differential equation. Just explain the first 2 steps

Answer 1

(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