dy'/dx= 1+y'^2

dy'/( 1+y'^2)=dx

Arctany'=x+C 1, (C 1 is a constant).

y'=tan(x+C 1)，dy/dx=tan(x+C 1)

dy=tan(x+C 1)dx

Y =-ln | cos (x+c 1) |+C2, (c 1, C2 is a constant).