DSolve[Derivative[1][y][x] == ((x + Sqrt[y[x]] - y[x])*y[x]^(3/2))/(x^3 - 3*x^2*y[x] + x*y[x]^(3/2) + y[x]^2 + 3*x*y[x]^2 - y[x]^(5/2) - y[x]^3),y[x],x]
dsolve(diff(y(x),x) = y(x)^(3/2)*(x-y(x)+y(x)^(1/2))/(y(x)^(3/2)*x-y(x)^(5/2)+y(x)^2+x^3-3*x^2*y(x)+3*x*y(x)^2-y(x)^3),y(x))