помогите решить xy' =y + √(x^2-y^2)

Однородное уравнение.
xy' =y + √(x²-y²) => y' =y/x + √(1-y²/x²)
y=tx => y’=t’x+t
t’x+t=t+√(1-t²) => t’x=√(1-t²)
dt/(1-t²)=dx/x => ∫dt/(1-t²)=∫dx/x
½•ln|(1+t)/(1-t)|=ln|x|+C => ln|(1+t)/(1-t)|=lnCx²
-1+1/(1-t)=Cx² => 1-t=1/(Cx²+1) => t=1-1/(Cx²+1)
y/x=(Cx²+1-1)/(Cx²+1) => y=Cx³/(Cx²+1)