Помогите решить y'(1+x+y)^(1/2)=x+y-1

x+y +1= z; dy/dx= dzdx - 1;
dz/dx* (z)^(1/2) = z-2+sqrt(z)

Переменные разделились .
1/3*ln(-1+z)+2/3*ln(z-4)-2/3*arctanh(z^(1/2))
+4/3*arctanh(1/2*z^(1/2)) = x + C;

1/3*ln(-1+z)+2/3*ln(z-4) –
2/3*arctanh(z^(1/2))
+4/3*arctanh(1/2*z^(1/2)) = x + C;

ln((x+y -3)^2/(x+y))^(1/3) -2/3*arctanh((x+y +1)^(1/2))
+4/3*arctanh(1/2*(x+y +1)^(1/2)) = x + C;
Проверь, простое интегрирование