Singular Solutions of Equations

Find the singular solution of the equation $y=xy'+y'+y'^{2}$.

Find the singular solution of the equation $(xy'-y)^{2}=x^{3}(2y-xy')$.

Find the singular solution of the equation $(xy'+y)^{2}+3x^{5}(xy'-2y)=0$.

Find the singular solution of the equation $2xy(1+y'^{2})-(xy'+y)^{2}=0$.

Find the singular solution of the equation $x^{2}y'^{2}-2(xy-2)y'+y^{2}=0$.

Find the singular solution of the equation $(y-xy')(ay'-b)=aby'$.

Find the singular solution of the equation $y'^{2}-yy'+e^{x}=0$.

Find the singular solution of the equation $y=xy'+\sqrt{1-y'^{2}}$.

Find the singular solution of the equation $y'^{2}-2xy'\sqrt{y}+4y\sqrt{y}=0$.

Find the singular solution of the equation $xy^{2}y'^{2}-y^{3}y'+a^{2}x=0$.