dsolve(-2*x*y(x)*(1-x)*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x)+x*(1-x)*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*y(x)*(1-y(x))*(x^2+y(x)-2*x*y(x))*diff(y(x),x)-y(x)^2*(1-y(x))^2-f*(y(x)*(-1+y(x))*(y(x)-x))^(3/2)=0,y(x))