Verify that `y=-x-1` is a solution of the differential equation `(y-x)dy-(y^2-x^2)dx=0.`

Explanation

Given, `y=-x-1`


`(dy)/(dx)=-1`


`LHS: (y-x)dy-(y^2-x^2)dx`


`=-(y-x)dx-(y^2-x^2)dx`


`=-dx[(y-x)+(y^2-x^2)]`


`=-dx[(y-x)+(y-x)(y+x)]`


`=-dx(y-x)(1+y+x)`


`=-dx(-x-1-x)(1-x-1+x)`


...