Question

Solve differential equation. Just explain the first 2 steps

Answer 1

(1) will write us of the following form


`(dy)/(dx)+y^2\sin x=0\\ \\`

(2) [do not it need explanation]


`(dy)/(dx)=-y^2\sin x\\ \\`

(3) Left place variable "y" and right place, variable "x" like this


`(dy)/(y^2)=-\sin x\, dx\\ \\`

(4) Integrate both members


`\displaystyle \int (dy)/(y^2)=\int-\sin x\, dx\\ \\`

(5) Solve us the integrals


`-(1)/(y)= \cos x+C`

(6) Isolate variable "y"


`\boxed{y=-(1)/(\cos x+C)}`

C: any cosntant