The straight line solution of Clairaut differential equation $y=(x+1)y^{\text{'}}+(y^{\text{'}}{)}^2$ is

A$)y=c(x+1)+c^2$

B$)y=cx+c^2$

C$)y=x^2+c$

D$)y=cx+c$

E$)$ None

A A

B$.B$

C $C$

D$.$ D

E$.$ E